Localization for Involutions in Floer Cohomology
We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smi...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2012
|
| Online Access: | http://hdl.handle.net/1721.1/71593 https://orcid.org/0000-0003-1628-1591 |
| _version_ | 1811084650861297664 |
|---|---|
| author | Seidel, Paul Smith, Ivan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Seidel, Paul Smith, Ivan |
| author_sort | Seidel, Paul |
| collection | MIT |
| description | We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included. |
| first_indexed | 2024-09-23T12:54:56Z |
| format | Article |
| id | mit-1721.1/71593 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:54:56Z |
| publishDate | 2012 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/715932022-09-28T10:51:37Z Localization for Involutions in Floer Cohomology Seidel, Paul Smith, Ivan Massachusetts Institute of Technology. Department of Mathematics Seidel, Paul Seidel, Paul We consider Lagrangian Floer cohomology for a pair of Lagrangian submanifolds in a symplectic manifold M. Suppose that M carries a symplectic involution, which preserves both submanifolds. Under various topological hypotheses, we prove a localization theorem for Floer cohomology, which implies a Smith-type inequality for the Floer cohomology groups in M and its fixed point set. Two applications to symplectic Khovanov cohomology are included. National Science Foundation (U.S.) (grant DMS-0405516) National Science Foundation (U.S.) (grant DMS-065260) European Research Council (grant ERC-2007-StG-205349) 2012-07-12T15:53:53Z 2012-07-12T15:53:53Z 2010-10 2010-08 Article http://purl.org/eprint/type/JournalArticle 1016-443X 1420-8970 http://hdl.handle.net/1721.1/71593 Seidel, Paul, and Ivan Smith. “Localization for Involutions in Floer Cohomology.” Geometric and Functional Analysis 20.6 (2010): 1464–1501. Web. https://orcid.org/0000-0003-1628-1591 en_US http://dx.doi.org/10.1007/s00039-010-0099-y Geometric and Functional Analysis Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Seidel, Paul Smith, Ivan Localization for Involutions in Floer Cohomology |
| title | Localization for Involutions in Floer Cohomology |
| title_full | Localization for Involutions in Floer Cohomology |
| title_fullStr | Localization for Involutions in Floer Cohomology |
| title_full_unstemmed | Localization for Involutions in Floer Cohomology |
| title_short | Localization for Involutions in Floer Cohomology |
| title_sort | localization for involutions in floer cohomology |
| url | http://hdl.handle.net/1721.1/71593 https://orcid.org/0000-0003-1628-1591 |
| work_keys_str_mv | AT seidelpaul localizationforinvolutionsinfloercohomology AT smithivan localizationforinvolutionsinfloercohomology |