Symplectic Cohomology and q-Intersection Numbers

By P. Seidel, Jake Solomon. Geometric and Functional Analysis, 2010

51 citations recorded by the source corpus.

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document} -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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f1cff250a3d9c9ea3449473a1766c19cf555e940

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In Geometry and Topology

  1. P. Seidel
  2. D. Auroux
  3. M. Abouzaid
  4. I. Smith
  5. Alexander F. Ritter
  6. Frederick J. Bourgeois III
  7. Mark McLean
  8. A. Oancea

In Mathematical Physics

  1. P. Seidel
  2. D. Auroux
  3. M. Abouzaid
  4. I. Smith
  5. Alexander F. Ritter
  6. Mark McLean
  7. A. Oancea
  8. Frederick J. Bourgeois III

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