Project/Area Number  09640095 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Geometry

Research Institution  HOKKAIDO UNIVERSITY 
Principal Investigator 
ONO Kaoru Grad.School of Sci., Hokkaido Univ.Prof., 大学院・理学研究科, 教授 (20204232)

CoInvestigator(Kenkyūbuntansha) 
KANDA Yutaka Grad.School of Sci., Hokkaido Univ.Inst., 大学院・理学研究科, 助手 (30280861)
OHTA Hiroshi Grad.School of Math., Nagoya Univ.Asso.Prof., 大学院・多元数理科学研究科, 助教授 (31400070)
FUKAYA Kenji Grad.School of Sci., Kyoto Univ.Prof., 大学院・理学研究科, 教授 (30165261)
大場 清 お茶の水女子大学, 理学部, 助手 (80242337)
TSUKADA Kazumi Fac.of Sci., Ochanomizu Univ.Prof., 理学部, 教授 (30163760)
IZUMIYA Shyuichi Grad.School of Sci., Hokkaido Univ.Prof., 大学院・理学研究科, 教授 (80127422)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 1998 : ¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1997 : ¥2,000,000 (Direct Cost : ¥2,000,000)

Keywords  Symplectic structure / contact structure / Jholomorphic curves / Floer homology / GromovWitten invariant / Lagrangian submanifold / SeibergWitten invariant / symplectic構造 / 接触構造 / J正則曲線 / Floerホモロジー / GromovWitten不変量 / ラグランジュ部分多様体 / SeibergWittem不変量 / symplectic 構造 / Floer ホモロジー / GromovWitten 不変量 / SeibergWitten 不変量 / Symplectic 構造 / ラグランジアン部分多様体 
Research Abstract 
Fukaya and Ono had introduced the notion of Kuranishi structure and constructed Floer homology for periodic Hamiltonian systems and GromovWitten invariants. We continue this direction and proceeded to investigation on Floer homology of Lagrangian intersections and ALPHA_*category proposed by Fukaya. In order to deal with transversality for the defining equation of the moduli space of holomorphic maps, we need to use multivalued perturbations and should work with rational coefficients. Hence we need to give coherent orientation for various moduli spaces. We showed that a spin structure on the lagrangian submanifold gives & natural orientation on moduli spaces. We also have another problem, namely there are examples of a pair of Lagrangian submanifolds so that the usual definition of the boundary operator for Floer complex does not give the boundary operator. We consider the boundary values of holomorphic disks systematically and defined a sort of obstruction classes for defining Floer homology for pairs of Lagrangian submanifolds. It is also shown that if such obstruction classes vanish, we can modify the definition of the boundary operator and define Floer homology. This is a result due to Fukaya, Kontsevich, Oh, Ohta and Ono. Ohta and Ono studied topology of symplectically filling 4manifold of links of simple singularities. Based on Taubes' theorem, we got a partial result in this direction. Inspired by this work, Kanda extended Taubes' result to certain noncompact symplectic manifolds.
