New development of geometry based on topological field theory

• Project/Area Number: 18104001
• Research Category: Grant-in-Aid for Scientific Research (S)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: FUKAYA Kenji 京都大学, 大学院・理学研究科, 教授 (30165261)
• Co-Investigator(Kenkyū-buntansha): NAKAJIMA Hiraku 京都大学, 数理解析研究所, 教授 (00201666) ; KONO Akira 京都大学, 大学院・理学研究科, 教授 (00093237) ; KATO Tsuyoshi 京都大学, 大学院・理学研究科, 教授 (20273427) ; UE Masaaki 京都大学, 大学院・理学研究科, 教授 (80134443) ; KATO Fumiharu 京都大学, 大学院・理学研究科, 准教授 (50294880) ; OHTA Shin-ichi 京都大学, 大学院・理学研究科, 准教授 (00372558) ; 小野 薫 北海道大学, 大学院・理学研究院, 教授 (20204232) ; 太田 啓史 名古屋大学, 大学院・多元数理科学研究科, 教授 (50223839) ; 齋藤 政彦 (齊藤 政彦) 神戸大学, 理学部, 教授 (80183044)
• Project Period (FY): 2006 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥82,160,000 (Direct Cost: ¥63,200,000、Indirect Cost: ¥18,960,000); Fiscal Year 2010: ¥19,240,000 (Direct Cost: ¥14,800,000、Indirect Cost: ¥4,440,000); Fiscal Year 2009: ¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000); Fiscal Year 2008: ¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000); Fiscal Year 2007: ¥13,910,000 (Direct Cost: ¥10,700,000、Indirect Cost: ¥3,210,000); Fiscal Year 2006: ¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000)
• Keywords: シンプレクティック多様体 / ミラー対称性 / フレアーホモロジー / シンプレクティク幾何 / 擬正則曲線 / モジュライ空間 / トーリック多様体 / ハミルトン力学系 / ラグランジュ部分多様体 / シンプレクティック幾何学 / 量子コホモロジー / ミラ-対称性 / フレア-ホモロジ- / カラビヤウ多様体 / 特異点理論 / ホモロジー代数 / 超弦理論 / 幾何学 / トポロジー / 数理物理 / 素粒子論 / 解析学 / 弦理論

Research Abstract

We studied Lagrangian Floer homology, its calculation and applications. We established the definition of it in the most general situation, and established various fundamental structure theorems. We calculate it in the case of toric manifolds etc, and applied it to both symplectic topology and Mirror symmetry

Research Products

• [Journal Article] Anchored Lagrangian submanifolds and their Floer theory (2010)
  • Author(s): K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono
  • Journal Title: Mirror symmetry and tropical geometry Volume: 527 Pages: 15-54
• [Journal Article] Cyclic symmetry and adic convergence in Lagrangian Floer theory (2010)
  • Author(s): K. Fukaya
  • Journal Title: Kyoto J. Math Volume: 50, no.3 Pages: 521-590
• [Journal Article] Differentiable operad, Kuranishi correspondence, and Foundation of topological field theories based on pseudo-holomorphic curves (2010)
  • Author(s): K. Fukaya
  • Journal Title: Arithmetic and geometry around quantization Volume: 279 Pages: 123-200
• [Journal Article] Lagrangian Floer theory on compact toric manifolds I (2010)
  • Author(s): K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono
  • Journal Title: Duke Math. J Volume: 151, no.1 Pages: 23-174
  • NAID: 120002598755
• [Journal Article] Anchored Lagrangian submanifolds and their Floer theory (2010)
  • Author(s): K.Fukaya, Y.-G.Oh, H.Ohta, K.Ono
  • Journal Title: Contemp.Math. Volume: 527 Pages: 15-54
  • Peer Reviewed
• [Journal Article] Cyclic symmetry and adic convergence in Lagrangian Floer theory (2010)
  • Author(s): K.Fukaya
  • Journal Title: Kyoto J.Math. Volume: 50 Pages: 521-590
  • Peer Reviewed
• [Journal Article] Differentiable operad, Kuranishi correspondence. and Foundation of topological field theories based on pseudo-holomorphic curves (2010)
  • Author(s): K.Fukaya
  • Journal Title: Progr.Math. Volume: 279 Pages: 123-200
  • Peer Reviewed
• [Journal Article] Lagrangian Floer theory on compact toric manifolds I (2010)
  • Author(s): K.Fukaya, Y.-G.Oh, H.Ohta, K.Ono
  • Journal Title: Duke Math.J. Volume: 151 Pages: 23-174
  • NAID: 120002598755
  • Peer Reviewed
• [Journal Article] Lagrangian Floer theory on compact toric manifolds I (2010)
  • Author(s): Fukaya, Kenji ; Oh, Yong-Geun ; Ohta, Hiroshi ; Ono, Kaoru
  • Journal Title: Duke Math. J. 151 Pages: 23-174
  • NAID: 120002598755
  • Peer Reviewed
• [Journal Article] Canonical models of filtered$ A_{\infty}$-algebras and Morse complexes (2009)
  • Author(s): K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono
  • Journal Title: CRM Proc. Lecture Notes Volume: 49 Pages: 201-227
• [Journal Article] The symplectic geometry of cotangent bundles from a categorical viewpoint (2009)
  • Author(s): K. Fukaya, P. Seidel, I Smith
  • Journal Title: Homological mirror symmetry Volume: 757 Pages: 1-26
• [Journal Article] Canonical models of filtered $A_\infty$-algebras and Morse complexes. (2009)
  • Author(s): Fukaya, Kenji ; Oh, Yong-Geun ; Ohta, Hiroshi ; Ono, Kaoru
  • Journal Title: New perspectives and challenges in symplectic field theory, Amer. Math. Soc., CRM Proc. Lecture Notes 49 Pages: 201-227
  • Peer Reviewed
• [Journal Article] Canonical models of filtered A^∞-algebras and Morse complexes to appear CRM (2009)
  • Author(s): K. Fukaya, Y.G.-Oh, H. Ohta, K. Ono
  • Journal Title: Proceedings and Lecture Notes Volume 49(accepted)
  • Peer Reviewed
• [Journal Article] The symplectic Geometry of Cotangent bundle from a Categorical Viewpoint (2009)
  • Author(s): K. Fukaya, P. Seidel, I. Smith
  • Journal Title: Homological Mirror symmetry, Lectures notes in Physics 757 Pages: 1-26
  • Peer Reviewed
• [Journal Article] Canonical models of filtered A^∞-algebras and Morse complexes (2009)
  • Author(s): K. Fukaya, Y. G. -Oh, H. Ohta, K. Ono
  • Journal Title: CRM Proceedings and Lecture Notes 49
  • Peer Reviewed
• [Journal Article] The symplectic Geometry of Cotangent bundle from a Categorical Viewpoint (2009)
  • Author(s): K. Fukaya, P. Seidel, I. Smith
  • Journal Title: Lectures notes in Physics 756 Pages: 1-26
  • Peer Reviewed
• [Journal Article] Loop space and holomorphic disc -summary- (2009)
  • Author(s): K. Fukaya
  • Journal Title: Proceeding of International Congress of Chinese Mathematics
• [Journal Article] Exact Lagrangian submanifolds in simply-connected cotangent bundles (2008)
  • Author(s): K. Fukaya, P. Seidel, I Smith
  • Journal Title: Invent. Math Volume: 172, no.1 Pages: 1-27
• [Journal Article] Exact Lagrangian submanifolds in simplly connected cotangent bundles (2008)
  • Author(s): K. Fukaya, P. Seidel, I. Smith
  • Journal Title: Invent. Math 172 Pages: 1-27
  • Peer Reviewed
• [Journal Article] Instanton counting and Donaldson invariants. J. Differential Geom (2008)
  • Author(s): L. Gottsche, H. Nakajima, K. Yoshioka
  • Journal Title: 80 (2008), no. 3 Pages: 343-390
  • Peer Reviewed
• [Journal Article] Mod pdecompositions of non-simply connected Lie groups (2008)
  • Author(s): D. Kishimoto, A. Kono
  • Journal Title: J. Math. Kyoto Univ 48 Pages: 1-5
  • Peer Reviewed
• [Journal Article] Exact Lagrangian submanifolds in simply connected cotangent bundle (2008)
  • Author(s): Kenji Fukaya, P. Seidel I. Smith
  • Journal Title: Invent. Math. 172 Pages: 1-27
  • Peer Reviewed
• [Journal Article] Loop space and holomorp hic disc -summary- (2007)
  • Author(s): K. Fukaya
  • Journal Title: to appear in proceedings of ICCM 2007
  • Peer Reviewed
• [Journal Article] Sheaves on ALE spaces and quiver varieties (2007)
  • Author(s): Hiraku Nakajima
  • Journal Title: Mosc. Math. J. 7 Pages: 699-722
  • Peer Reviewed
• [Journal Article] Cristal, canonical and PBW basis of quantum affine algebras (2007)
  • Author(s): Hiraku Nakajima
  • Journal Title: Algebraic group and homogeneous spaces (Tata Institute)論文集 Pages: 389-421
  • Peer Reviewed
• [Journal Article] Application of Floer homology of Lagrangian submanifolds to Symplectic Topology (2006)
  • Author(s): K. Fukaya
  • Journal Title: Morse theoretic methods in nonlinear analysis and in symplectic topology Volume: 217 Pages: 231-276
• [Journal Article] Floer homo logy in symplectic geometry and in mirror symmetry (2006)
  • Author(s): Y.-G. Oh and K. Fukaya
  • Journal Title: International Congress of Mathematicians(Eur. Math. Soc., Zurich) Vol.II Pages: 879-905
  • Peer Reviewed
• [Journal Article] Floer homology in symplectic geometry and in mirror symmetry. International Congress of Mathematicians (2006)
  • Author(s): Y.G.-Oh, K.Fukaya
  • Journal Title: Eur. Math. Soc., Zurich Vol. II Pages: 879-905
• [Journal Article] Floer Novikov homology and the flux conjecture (2006)
  • Author(s): Kaoru Ono
  • Journal Title: Geometric and Functional Analysis 16 Pages: 981-1020
• [Journal Article] Moduli of stable parabolic connections Riemann Hilbert correspondence and Geometry of Painleve equiation of type IV I (2006)
  • Author(s): M.Inaba, K.Iwasaki, M.Saitoh
  • Journal Title: Publ. RIMS 42 Pages: 987-1089
• [Journal Article] Instanton counting on blowup. I. 4-dimensional pure gauge theory. (2005)
  • Author(s): H.Nakajima, Hiraku, K.Yoshioka
  • Journal Title: Invent. Math. 162-2 Pages: 313-355
• [Journal Article] Cyclic symmetry and adic convergence in Lagrangian Floer theory.
  • Author(s): Kenji Fukaya
  • Journal Title: Kyoto Journal of Math. (to appear(accepted))
  • Peer Reviewed
• [Journal Article] Symplectic geometry of cotangent bundle from a categorical point of view
  • Author(s): Kenji Fukaya, P. Seidel I. Smith
  • Journal Title: Homological Mirror symmetry (ed. A. Kapustin, M. Kreuzer, K. -G. Schlesinger) Birkhauser.論文集 (掲載決定) Pages: 1-26
  • Peer Reviewed
• [Journal Article] Loop space and holomorphic disc-summary-
  • Author(s): Kenji Fukaya
  • Journal Title: Proc. Of International Congress of Chinese Math.論文集 (掲載決定)
• [Journal Article] Differential operad, Kuranishi correspondence, and Foundation of topological field theories based on pseudo-holomorphic curve
  • Author(s): Kenji Fukaya
  • Journal Title: Proc. of AGAQ conference (ed. M. Marcolli, Y. Mannin, O Ceyhan) Birkhauser.論文集 (掲載決定)
  • Peer Reviewed
• [Journal Article] The symplectic geometry of cotangent bundles from a categorical viewpoint
  • Author(s): K.Fukaya, P.Seidel, I.Smith
  • Journal Title: The Proc. of Mirror symmetry conference in Schroedinger institute. (to appear)(accepted)
• [Journal Article] Differentiable operad, Kuranishi correspondence, and Foundation of topological field theories based on pseudo-holomorphic curve
  • Author(s): K.Fukaya
  • Journal Title: The Proc. of Arithmetic and Geometry Around Quantization-Istanbul (to appear)(accepted)
• [Presentation] ラグランジュ部分多様体のフレアーホモロジーの計算と応用 (2010)
  • Author(s): K. Fukaya
  • Organizer: 京都大学大談話会
  • Place of Presentation: 京都大学
  • Year and Date: 2010-11-17
• [Presentation] ラグランジュ部分多様体のフレアーホモロジーの計算と応用 (2010)
  • Author(s): K.Fukaya
  • Organizer: 京都大学大談話会
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2010-11-17
• [Presentation] Calculations and applications of Lagrangian Floer cohomology (2010)
  • Author(s): K. Fuakya
  • Organizer: Dynamical Systems to Symplectic Topology Conference in honour of Edi Zehnder on the occasion of his 70th birthday
  • Place of Presentation: ETH Zurich(スイス)
  • Year and Date: 2010-11-12
• [Presentation] Calculations and applications of Lagrangian Floer cohomology (2010)
  • Author(s): K.Fukaya
  • Organizer: From Dynamical Systems to Symplectic Topology Conference in honour of Edi Zehnder on the occasion of his 70th birthday
  • Place of Presentation: ETH Zurich(スイス)(招待講演)
  • Year and Date: 2010-11-12
• [Presentation] Homological mirror symmetry between toric A model and Landau-Ginzburg B model (2010)
  • Author(s): K. Fuakya
  • Organizer: Hayashibara Forum
  • Place of Presentation: 京大数理研
  • Year and Date: 2010-11-05
• [Presentation] Homological mirror symmetry between toric A model and Landau-Ginzburg B model (2010)
  • Author(s): K.Fukaya
  • Organizer: Hayashibara Forum
  • Place of Presentation: 京大数理研(招待講演)
  • Year and Date: 2010-11-05
• [Presentation] Hochschild and cyclic cohomology in Lagrangian Floer theory and Mirror symmetry (2010)
  • Author(s): K. Fukaya
  • Organizer: Higher structure in Math. and Physics
  • Place of Presentation: Schrodinger institute(オーストリア)
  • Year and Date: 2010-10-25
• [Presentation] Hochschild and cyclic cohomology in Lagrangian Floer theory and Mirror symmetry (2010)
  • Author(s): K.Fukaya
  • Organizer: Higher structure in Math.and Physics 2010
  • Place of Presentation: Schrodinger institute(オーストリア)(招待講演)
  • Year and Date: 2010-10-25
• [Presentation] Mirror symmetry between Toric A model and Landau-Gizburg B model (2010)
  • Author(s): K. Fuakya
  • Organizer: Yamabe symposium
  • Place of Presentation: University of Minesota(アメリカ)
  • Year and Date: 2010-10-10
• [Presentation] Mirror symmetry between Toric A model and Landau-Gizburg B model (2010)
  • Author(s): K.Fukaya
  • Organizer: Yamabe symposium
  • Place of Presentation: University of Minesota(アメリカ)(招待講演)
  • Year and Date: 2010-10-10
• [Presentation] Anti-holomorphic involution in Lagrangian Floer theory (2010)
  • Author(s): K. Fuakya
  • Organizer: STRUCTURES REELLES SUR LES VARIETES COMPLEXES : RESULTATS ET PERSPECTIVES
  • Place of Presentation: Luminy(フランス)
  • Year and Date: 2010-06-16
• [Presentation] Anti-holomorphic involution in Lagrangian Floer theory (2010)
  • Author(s): K.Fukaya
  • Organizer: STRUCTURES REELLES SUR LES VARIETES COMPLEXES : RESULTATS ETPERSPECTIVES
  • Place of Presentation: Luminy(フランス)(招待講演)
  • Year and Date: 2010-06-16
• [Presentation] Lagrangian Floer theory and Mirror symmetry (2010)
  • Author(s): K. Fukaya
  • Organizer: HSIUNG INTERNATIONAL SYMPOSIUM IN GEOMETRY AND TOPOLOGY
  • Place of Presentation: Lehigh University(アメリカ)
  • Year and Date: 2010-05-28
• [Presentation] Lagrangian Floer theory and Mirror symmetry (2010)
  • Author(s): K.Fukaya
  • Organizer: C.-C.HSIUNG INTERNATIONAL SYMPOSIUM IN GEOMETRY AND TOPOLOGY
  • Place of Presentation: Lehigh University(アメリカ)(招待講演)
  • Year and Date: 2010-05-28
• [Presentation] Mirror symmetry for toric manifold and singularity theory on Novikov ring 他2件 (2009)
  • Author(s): 深谷賢治
  • Organizer: 北京大学談話会
  • Place of Presentation: 北京大学
  • Year and Date: 2009-03-25
• [Presentation] Mirror symmetry of topic manifolds (2009)
  • Author(s): 深谷賢治
  • Organizer: Work shop on Homological Mirror symmetry and related topics
  • Place of Presentation: マイアミ大学
  • Year and Date: 2009-03-21
• [Presentation] K. Saitoh theory on Novikov ring (2008)
  • Author(s): 深谷賢治
  • Organizer: CBMS workshop Toropical geometry and Mirror symmetry
  • Place of Presentation: カンザス州立大学
  • Year and Date: 2008-12-17
• [Presentation] Lagrangian Floer homology and Mirror symmetry (2008)
  • Author(s): 深谷賢治
  • Organizer: Brent P. Smith Memorial Lecture, Kansas state University
  • Place of Presentation: カンザス州立大学
  • Year and Date: 2008-12-12
• [Presentation] Lagrangian Floer cohomology on toricmanifold (2008)
  • Author(s): 深谷賢治
  • Organizer: Geometry seminar at Univ. Mineapolis
  • Place of Presentation: ミネアポリス大学
  • Year and Date: 2008-12-10
• [Presentation] Various aspects and approaches to chain level string topology (2008)
  • Author(s): 深谷賢治
  • Organizer: Higher structure conference
  • Place of Presentation: ペルヌイセンター
  • Year and Date: 2008-11-05
• [Presentation] Mirror symmetry of toric A-model and Landau-Ginzburg B-model (2008)
  • Author(s): 深谷賢治
  • Organizer: Perspectives in Mathematical Sciences
  • Place of Presentation: 慶応大学
  • Year and Date: 2008-10-11
• [Presentation] Lagrangian Floer theory via example of Toric manifolds (2008)
  • Author(s): 深谷賢治
  • Organizer: Holomorphic curves : algebraic structures and geometric application
  • Place of Presentation: スタンフォード大学
  • Year and Date: 2008-08-24
• [Presentation] Mirror symmetry of toric A model and LG B-model (2008)
  • Author(s): 深谷賢治
  • Organizer: Concluding conference of the program Real and Tropical Algebraic Geometry
  • Place of Presentation: ベルヌイセンター
  • Year and Date: 2008-06-20
• [Presentation] Lagrangian Floer Theory on Toric Manifolds (2008)
  • Author(s): 深谷賢治
  • Organizer: Higher structure conference
  • Place of Presentation: モントリオール大学
  • Year and Date: 2008-05-20
• [Presentation] Symplectic Geometry of Lagrangian submanifold (2008)
  • Author(s): Kenji Fukaya
  • Organizer: Opening Symposium
  • Place of Presentation: 数物連携宇宙機構
  • Year and Date: 2008-03-10
• [Presentation] Moduli of monodromy stokes data for Painleve equations (2008)
  • Author(s): Masahiko Saitoh
  • Organizer: Math-Physics Joint seminar 2007-2008
  • Place of Presentation: University of Pennsylvannia
  • Year and Date: 2008-03-07
• [Presentation] Conjectural triplly graded link homology groups of the Hopf link and Hilbert schemes of points on the plane (2008)
  • Author(s): Hiraku Nakajima
  • Organizer: Princeton University Symplectic geometry seminar
  • Place of Presentation: Princeton University
  • Year and Date: 2008-02-29
• [Presentation] Floer theory of orbits in toric manifolds (2008)
  • Author(s): Kenji Fukaya
  • Organizer: New developments in Algebraic Geometry, Integrable system and Mirror symmetry
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2008-01-08
• [Presentation] Loop space and holomorphic disc (2007)
  • Author(s): Kenji Fukaya
  • Organizer: International Congress of Chinese Math.
  • Place of Presentation: Hanzhou University
  • Year and Date: 2007-12-20
• [Presentation] Phenomenon of Tropical flavor in Lagrangian Floer theory (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Tropical Geometry
  • Place of Presentation: Mathematisches Forschungsinsinstitute Oberwolfach
  • Year and Date: 2007-10-12
• [Presentation] Instanton counting and knot invariants (2007)
  • Author(s): Hiraku Nakajima
  • Organizer: New connections of representation theory to algebraic geometry and physics
  • Place of Presentation: プリンストン大学高等研究所
  • Year and Date: 2007-09-28
• [Presentation] An analogue of Flux conjecture for Lagrangian submanifold (2007)
  • Author(s): Kaoru Ono
  • Organizer: Conference on Symplectic geometry and Physics
  • Place of Presentation: チューリッヒ工科大学
  • Year and Date: 2007-09-07
• [Presentation] Homotopy theory of A infinity algebras I (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Toward relative symplectic Field theory
  • Place of Presentation: ニューヨーク市立大学
  • Year and Date: 2007-09-07
• [Presentation] Homotopy theory of A infinity algebras II (2007)
  • Author(s): Hiroshi Ohta
  • Organizer: Toward relative symplectic Field theory
  • Place of Presentation: ニューヨーク市立大学
  • Year and Date: 2007-09-07
• [Presentation] Homotopy theory of A infinity algebras III (2007)
  • Author(s): Kaoru Ono
  • Organizer: Toward relative symplectic Field theory
  • Place of Presentation: ニューヨーク市立大学
  • Year and Date: 2007-09-07
• [Presentation] L infinity differential operad, string topology and pseudo-holomorphic discs (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Conference on Symplectic geometry and Physics
  • Place of Presentation: チューリッヒ工科大学
  • Year and Date: 2007-09-03
• [Presentation] Mirror symmetry of Abelian varieties (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Workshop on homological Mirror symmetry and related matter
  • Place of Presentation: ベルヌーイセンター(ローザンヌ)
  • Year and Date: 2007-08-28
• [Presentation] L infinity piecewise differentiable operad and transversality problem in string topology (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Pasific Rim complex geometry conference
  • Place of Presentation: ホテル北野プラザ六甲荘
  • Year and Date: 2007-08-12
• [Presentation] Wall crossing formula for Donaldson invariants and instanton counting (2007)
  • Author(s): Hiraku Nakajima
  • Organizer: Pasific Rim complex geometry conference
  • Place of Presentation: ホテル北野プラザ六甲荘
  • Year and Date: 2007-08-10
• [Presentation] Lagrangian Floer theory (2007)
  • Author(s): Kenji Fukaya
  • Organizer: International conference on Geometry and Analysis
  • Place of Presentation: 南京大学
  • Year and Date: 2007-08-06
• [Presentation] Floer theory for Lagrangian submanifolds (2007)
  • Author(s): Kaoru Ono, Y.G, -Oh
  • Organizer: Conference on New Challenges and Perspectives in Symplectic Field theory
  • Place of Presentation: スタンフォード大学
  • Year and Date: 2007-06-28
• [Presentation] Lagrangian Floer theory in the case of Real point set II (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Real Tropical and complex enumerative Geometry
  • Place of Presentation: モントリオール大学数学研究センター
  • Year and Date: 2007-06-20
• [Presentation] Lagrangian Floer theory in the case of Real point set I (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Real Tropical and complex enumerative Geometry
  • Place of Presentation: モントリオール大学数学研究センター
  • Year and Date: 2007-06-19
• [Presentation] Normally polynomial Perturbation revisited (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Birds Workshop on Floer homology
  • Place of Presentation: Banff Research center
  • Year and Date: 2007-05-15
• [Presentation] Kuranishi correspondence and foundation of various topologica I field theories (2007)
  • Author(s): Kenji Fukaya
  • Organizer: Recent development in symplectic topology
  • Place of Presentation: クレイ研究所(ボストン)
  • Year and Date: 2007-04-22
• [Book] Lagrangian intersection Floer theory : anomaly and obstruction. Part I. AMS/IP Studies in Advanced Mathematics, 46. 1. American Mathematical Society, Providence, RI (2009)
  • Author(s): K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono
  • Publisher: International Press
• [Book] Lagrangian intersection Floer theory : anomaly and obstruction. Part II. AMS/IP Studies in Advanced Mathematics, 46. 2. American Mathematical Society, Providence, RI (2009)
  • Author(s): K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono
  • Publisher: International Press
• [Book] Lagrangian intersection Floer theory : anomaly and obstruction (2009)
  • Author(s): Fukaya, Kenji ; Oh, Yong-Geun ; Ohta, Hiroshi ; Ono, Kaoru
  • Total Pages: 800
  • Publisher: American Mathematical Society and International Press
• [Book] シンプレクティック幾何学(講座からの単行本化) (2008)
  • Author(s): 深谷賢治
  • Total Pages: 414
  • Publisher: 岩波書店
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