Symplectic Cohomology and q-Intersection Numbers
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Seidel_Symplectic cohomology.pdf
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402.85 KB
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Adobe PDF
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Author(s)
Seidel, Paul
Solomon, Jake P.
Date Issued
May 2012
Journal
Geometric and Functional Analysis
Publisher
Springer-Verlag
Citation
Seidel, Paul, and Jake P. Solomon. “Symplectic Cohomology and q-Intersection Numbers.” Geometric and Functional Analysis 22, no. 2 (April 23, 2012): 443-477.
Version
Original manuscript
Abstract
Given a symplectic cohomology class of degree 1, we define the notion of an “equivariant" Lagrangian submanifold (this roughly corresponds to equivariant coherent sheaves under mirror symmetry). The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces an R-grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the “dilation" condition stipulating that the BV operator applied to the symplectic cohomology class gives the identity.
Description
Original manuscript March 21, 2012
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-012-0159-6
