3-manifold invariants as viewed from triangulations

• Project/Area Number: 21740045
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: KODA Yuya 東北大学, 大学院・理学研究科, 助教 (20525167)
• Project Period (FY): 2009 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 3次元多様体 / 四面体分割 / 絡み目 / 量子不変量 / 結び目 / 不変量 / ハンドル体 / グラフ / 写像類群 / Heegaard 分解 / 空間グラフ / 位相的場の理論

Research Abstract

Using triangulations equipped with certain additional structures, we obtained formulae for the Reidemeister-Turaev torsion of standard Spin-c structures for Seifert fibered3-manfolds and colored Turaev-Viro invariants for twist knots in the 3-spheres and torus knots in lens spaces. Moreover, we gave an upper bounds of the complexities for the twist knots in lens spaces and described the hyperbolic structures of their strongly cyclic branched covering spaces.

Research Products

• [Journal Article] Topological symmetry groups and mapping class groups for spatial graphs (2013)
  • Author(s): Sangbum Cho, Yuya Koda
  • Journal Title: Michigan Mathematical Journal Volume: 62 Pages: 131-142
  • Peer Reviewed
• [Journal Article] (2+1)-dimensional TQFT model for Colored Turaev-Viro invariants (2013)
  • Author(s): Yuya Koda, Taiji Taniguchi
  • Journal Title: International Mathematics Research Notices Volume: IMRN 2013 Issue: 1 Pages: 218-242
  • DOI: 10.1093/imrn/rnr238
  • Peer Reviewed
• [Journal Article] The Reidemeister-Turaev torsion of standard Spin^c structures on Seifert Fibered 3-manifolds (2012)
  • Author(s): Yuya Koda
  • Journal Title: Annales de la Faculte des Sciences de Toulouse. Mathematiques. Serie 6 21 Volume: 21 Issue: 4 Pages: 745-768
  • DOI: 10.5802/afst.1349
  • Peer Reviewed
• [Journal Article] Links and spines (2012)
  • Author(s): Yuya Koda
  • Journal Title: Journal of Knot Theory and its Ramifications 21 Volume: [27] Issue: 03 Pages: 1250027-1250027
  • DOI: 10.1142/s0218216511009674
  • Peer Reviewed
• [Journal Article] The Reidemeister-Turaev torsion of standard Spin^c structures on Seifert Fibered 3-manifolds (2012)
  • Author(s): Yuya Koda
  • Journal Title: Annales de la Faculte des Sciences de Toulouse. Serie VI. Mathematiques Volume: 21 Pages: 745-768
  • Peer Reviewed
• [Journal Article] Tunnel complexes of 3-manifolds (2011)
  • Author(s): Yuya Koda
  • Journal Title: Algebraic & Geometric Topology Volume: 11 Issue: 1 Pages: 417-447
  • DOI: 10.2140/agt.2011.11.417
  • Peer Reviewed
• [Journal Article] Topological symmetry groups and mapping class groups of spatial graphs (2011)
  • Author(s): 古宇田悠哉
  • Journal Title: HAKONE SEMINAR Volume: 27 Pages: 19-28
• [Journal Article] Tunnel complexes of 3-manifolds (2011)
  • Author(s): Yuya Koda
  • Journal Title: Algebr.Geom.Topol. Volume: 11 Pages: 417-447
  • Peer Reviewed
• [Journal Article] Colored Turaev-Viro invariants of twist knots (2009)
  • Author(s): Yuya Koda
  • Journal Title: Topology and its Applications Volume: 156 Pages: 577-593
  • URL: http://www.sciencedirect.com/science/article/pii/S0166864108002897.
  • Peer Reviewed
• [Journal Article] On the Reidemeister-Turaev torsion of standard Spin^c structures on Seifert fibered 3-manifolds
  • Author(s): Yuya Koda
  • Journal Title: RIMS Kokyuroku Volume: (未定)(to appear)
• [Journal Article] O-graphic study of closed 3-manifolds
  • Author(s): Yuya Koda
  • Journal Title: 箱根セミナ2010 Volume: (未定)(to appear)
• [Presentation] Primitive disk complexes and genus two Goeritz groups of all lens spaces (2012)
  • Author(s): Yuya Koda
  • Organizer: Seminari di Geometria, Universita di Pisa
  • Place of Presentation: イタリア
  • Year and Date: 2012-09-19
• [Presentation] Spring Workshop 2012 on Low-Dimensional Topology and its Ramifications Joint Workshop 「ハン ドル体結び目とその周辺 IV」 (2012)
  • Author(s): 古宇田悠哉
  • Organizer: 名城大学名駅サテライト
  • Place of Presentation: 名古屋
  • Year and Date: 2012-03-04
• [Presentation] ハンドル体結び目のシンメトリー群 (2012)
  • Author(s): 古宇田悠哉
  • Organizer: Spring Workshop 2012 on Low-Dimensional Topology and its Ramifications Joint Workshop「ハンドル体結び目とその周辺IV」
  • Place of Presentation: 名古屋
  • Year and Date: 2012-03-04
• [Presentation] チェーン絡み目の例外的手術について(Martelli-Petronio, Martellli-Petronio-Roukemaの仕事の解説) (2012)
  • Author(s): 古宇田悠哉
  • Organizer: 日大トポロジーセミナー
  • Place of Presentation: 日本大学，東京
  • Invited
• [Presentation] Primitive disk complexes and genus two Goeritz groups of all lens spaces (2012)
  • Author(s): 古宇田悠哉
  • Organizer: 低次元多様体北見セミナー(2012)
  • Place of Presentation: 北見工業大学，北海道
  • Invited
• [Presentation] Primitive disk complexes and genus two Goeritz groups of all lens spaces (2012)
  • Author(s): Yuya Koda
  • Organizer: Seminari di Geometria, Universita di Pisa
  • Place of Presentation: ピサ，イタリア
  • Invited
• [Presentation] Mapping class groups and topological symmetry groups of spatial graphs (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 研究集会「Graphと3次元多様体の研究」
  • Place of Presentation: 箱根
  • Year and Date: 2011-10-26
• [Presentation] 3 次元球面内のグラフとハ ンドル体の対称性について (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 東北大学幾 何セミナー, 東北大学
  • Place of Presentation: 仙台
  • Year and Date: 2011-10-17
• [Presentation] 3次元球面内のグラフとハンドル体の対称性について (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 東北大学幾何セミナー
  • Place of Presentation: 仙台
  • Year and Date: 2011-10-17
• [Presentation] Automorphisms of the3-sphere that preserve spatial graphs and handlebody-knots (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 早大理工トポロジーセミナー, 早稲田大学
  • Place of Presentation: 東京
  • Year and Date: 2011-08-29
• [Presentation] Automorphisms of the 3-sphere that preserve spatial graphs and handle body-knots (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 早大理工トポロジーセミナー
  • Place of Presentation: 東京
  • Year and Date: 2011-08-29
• [Presentation] Automorphisms of the3-sphere that preserve spatial graphs and handlebody-knots (2011)
  • Author(s): Yuya Koda
  • Organizer: Oberseminar Geometrie, Topologie und Analysis, University of Cologne
  • Place of Presentation: ドイツ
  • Year and Date: 2011-06-24
• [Presentation] Automorphisms of the 3-sphere that preserve spatial graphs and handlebody-knots (2011)
  • Author(s): Yuya Koda
  • Organizer: Oberseminar Geometrie, Topologie und Analysis
  • Place of Presentation: ドイツ,ケルン
  • Year and Date: 2011-06-24
• [Presentation] Automorphisms of the3-sphere that preserve knotted handlebodies of genus two (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 広島大学 トポロジー・幾何セミナー, 広島大学
  • Place of Presentation: 東広島
  • Year and Date: 2011-01-25
• [Presentation] Automorphisms of the 3-sphere that preserve knotted handlebodies of genus two (2011)
  • Author(s): 古宇田悠哉
  • Organizer: 広島大学トポロジー・幾何セミナー
  • Place of Presentation: 広島大学
  • Year and Date: 2011-01-25
• [Presentation] Automorphisms of the3-sphere that preserve knotted handlebodies of genus two (2010)
  • Author(s): 古宇田悠哉
  • Organizer: 上智トポロ ジー研究集会, 上智大学
  • Place of Presentation: 東京
  • Year and Date: 2010-12-25
• [Presentation] Automorphisms of the 3-sphere that preserve knotted handlebodies of genus two (2010)
  • Author(s): 古宇田悠哉
  • Organizer: 上智トポロジー研究集会
  • Place of Presentation: 上智大学
  • Year and Date: 2010-12-25
• [Presentation] O-graphic study of closed 3-manifolds (2010)
  • Author(s): 古宇田悠哉
  • Organizer: 研究集会「Graphと3次元多様体の研究」
  • Place of Presentation: 東洋大学箱根保養所
  • Year and Date: 2010-10-27
• [Presentation] On the Reidemeister-Turaev torsion of standard Spin^c structures on Seifert fibered 3-manifolds,"Twisted topological invariants and topology of low-dimensional manifolds" (2010)
  • Author(s): Yuya Koda
  • Organizer: 京都大学数理解析研究所 合宿型セミナー , あきた白神体験センター
  • Place of Presentation: 秋田
  • Year and Date: 2010-09-15
• [Presentation] On the Reidemeister-Turaev torsion of standard Spin$^c$ structures on Seifert fibered 3-manifolds (2010)
  • Author(s): Yuya Koda
  • Organizer: 京都大学数理解析研究所合宿型セミナー"Twisted to pological invariants and topology of low-dimensional manifolds"
  • Place of Presentation: あきた白神体験センター
  • Year and Date: 2010-09-15
• [Presentation] Introduction to colored Turaev-Viro invariants (2010)
  • Author(s): 古宇田悠哉
  • Organizer: Workshop: Lefschetz fibration and category theory, 大阪大学
  • Place of Presentation: 大阪
  • Year and Date: 2010-06-26
• [Presentation] Introduction to colored Turaev-Viro invariants (2010)
  • Author(s): Yuya Koda
  • Organizer: Workshop : Lefschetz fibration and category theory
  • Place of Presentation: 大阪大学
  • Year and Date: 2010-06-26
• [Presentation] 絡み目の色付きTuraev-Viro不変量と位相的場の理論 (2010)
  • Author(s): 古宇田悠哉
  • Organizer: 数学専攻談話会
  • Place of Presentation: 東北大学
  • Year and Date: 2010-04-12
• [Presentation] Quotients of disk complexes by group actions (2010)
  • Author(s): 古宇田悠哉
  • Organizer: 研究会「結 び目と3次元多様体」, 慶應義塾大学
  • Place of Presentation: 横浜
  • Year and Date: 2010-03-18
• [Presentation] Quotients of disk complexes by Goeritz group actions (2010)
  • Author(s): 古宇田悠哉
  • Organizer: 研究会「結び目と3次元多様体」
  • Place of Presentation: 横浜市
  • Year and Date: 2010-03-18
• [Presentation] Quotients of disk complexes by Goeritz group actions (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 東 北大学幾何セミナー, 東北大学
  • Place of Presentation: 仙台
  • Year and Date: 2009-11-24
• [Presentation] Quotients of disk complexes by Goeritz group actions (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 東北大学幾何セミナー
  • Place of Presentation: 仙台市
  • Year and Date: 2009-11-24
• [Presentation] Multiple disk complexes and Goeritz groups (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 研究集会「Graph と3次元多様体の研究」
  • Place of Presentation: 小田原市
  • Year and Date: 2009-10-28
• [Presentation] Colored Turaev-Viro invariants of twisted double-series and cable-series in lens spaces,「The first KOOK-TAPU Joint Seminar (TOP Seminar) on Knot Theory and Related Topics」 (2009)
  • Author(s): Yuya Koda
  • Organizer: 研究集会,大阪市立大学
  • Place of Presentation: 大阪
  • Year and Date: 2009-08-19
• [Presentation] Colored Turaev-Viro invariants of twisted double-series and cable-series in lens spaces (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 研究集会「The first KOOK-TAPU Joint Seminar(TOP Seminar)on Knot Theory and Related Topics」
  • Place of Presentation: 大阪市
  • Year and Date: 2009-08-19
• [Presentation] Tunnel complexes of 3-manifolds (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 日大トポロジーセミナー
  • Place of Presentation: 東京都
  • Year and Date: 2009-07-22
• [Presentation] Tunnel complexes of3-manifolds, Workshop "Simplicial Complexes Arising in Low-Dimensional Topology" (2009)
  • Author(s): Yuya Koda
  • Organizer: 東京工業大学
  • Place of Presentation: 東京
  • Year and Date: 2009-07-03
• [Presentation] Tunnel complexes of 3-manifolds (2009)
  • Author(s): 古宇田悠哉
  • Organizer: Workshop "Simplicial Complexes Arising in Low-Dimensional Topology"
  • Place of Presentation: 横浜市
  • Year and Date: 2009-07-03
• [Presentation] 3次元多様体のトンネル複体について (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 研究会「ハンドル体結び目とその周辺II」,大阪市立大学
  • Place of Presentation: 大阪
  • Year and Date: 2009-06-20
• [Presentation] 3次元多様体のトンネル複体について (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 研究会「ハンドル体結び目とその周辺II」
  • Place of Presentation: 大阪市
  • Year and Date: 2009-06-20
• [Presentation] Tunnel complexes of 3-manifolds (2009)
  • Author(s): 古宇田悠哉
  • Organizer: 早稲田大学教育学部トポロジーセミナー
  • Place of Presentation: 東京都
  • Year and Date: 2009-06-13
• [Remarks]
  • URL: http://www.math.tohoku.ac.jp/~koda/
• [Remarks]
  • URL: http://www.math.tohoku.ac.jp/~koda/works.html
• [Remarks]
  • URL: http://www.math.tohoku.ac.jp/~koda/works.html