|
|||||
|
|
|
|
|
|
|
|
|
Antisymplectic involution
and Floer cohomology
Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta and Kaoru Ono |
|
Geometry & Topology 21 (2017) 1–106
|
|
DOI: 10.2140/gt.2017.21.1
|
Abstract |
|
The main purpose of the present paper is a study of orientations of the moduli spaces of pseudoholomorphic discs with boundary lying on a real Lagrangian submanifold, ie the fixed point set of an antisymplectic involution on a symplectic manifold. We introduce the notion of –relative spin structure for an antisymplectic involution and study how the orientations on the moduli space behave under the involution . We also apply this to the study of Lagrangian Floer theory of real Lagrangian submanifolds. In particular, we study unobstructedness of the –fixed point set of symplectic manifolds and, in particular, prove its unobstructedness in the case of Calabi–Yau manifolds. We also do explicit calculation of Floer cohomology of over , which provides an example whose Floer cohomology is not isomorphic to its classical cohomology. We study Floer cohomology of the diagonal of the square of a symplectic manifold, which leads to a rigorous construction of the quantum Massey product of a symplectic manifold in complete generality. |
Keywords
symplectic Geometry, Lagrangian submanifold,
pseudoholomorphic curve, Floer cohomology, antisymplectic
involution, orientation, quantum cohomology, unobstructed
Lagrangian submanifolds
|
Mathematical Subject Classification 2010
Primary: 53D40, 53D45
Secondary: 14J33
|
References |
Publication
Received: 25 January 2010
Revised: 27 November 2015
Accepted: 3 January 2016
Published: 10 February 2017
Proposed: Gang Tian
Seconded: Yasha Eliashberg, Richard Thomas
|
Authors |
| Kenji Fukaya | |
| Simons Center for Geometry and
Physics State University of New York Stony Brook Stony Brook, NY 11794-3636 United States |
|
| Yong-Geun Oh | |
| Center for Geometry and
Physics Institute for Basic Sciences Pohang Gyungbuk, 37673 South Korea |
|
| Hiroshi Ohta | |
| Graduate School of Mathematics Nagoya University Nagoya 464-8602 Japan |
|
| Kaoru Ono | |
| Research Institute for Mathematical
Sciences Kyoto University Kyoto 606-8502 Japan |
|
|
