2005 Fiscal Year Final Research Report Summary
Floor homology, singularities and deformation theory
| Project/Area Number |
14340019
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
ONO Kaoru Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (20204232)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAGUCHI Keizo Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (00113639)
IZUMIYA Shyuichi Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (80127422)
ISHIKAWA Goo Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (50176161)
FUKAYA Kenji Kyoto Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (30165261)
OHTA Hiroshi Nagoya Univ., Grad.School of Math., Asso.Prof., 大学院・多元数理科学研究科, 助教授 (50223839)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Floer homology / symplectic structure / contact structure / singularity / pseudo holomorphic curve |
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| Research Abstract |
We studied Floer theory in symplectic geometry in both theoretical foundation and applications. We extend Floer theory for Hamiltonian systems to that for Lagrangian intersections. Namely, we introduce the nation of filtered A_∞-algebras, filtered A_∞-bimodule etc. and give geometric constructions. As applications, we studied non-triviality of the Maslov class of Lagrangian embeddings, Lagrangian intersection under Hamiltonian deformations, etc. We also prove the flux conjecture using Floer theory for symplectomosphisms. This conjecture is basic for understanding how the group of Hamiltonian diffeomorphisms in the group of symplectomosphisms. These results are written up as research papers, preprints during the term of project.
With Ohta, we tried to understand isolated singularities on complex surfaces through symplectic fillings of their links. In particular, we established uniquener of minimal symplectic fillings and studied its relation to Brieskorn's results for simple singularities. In the case of simple-elliptic singularities, we gave classification and interpreted Pinkham's result concerning the condition for existence of smoothings.
These results are published in research journals.
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