4.4 Article

Symplectic Cohomology and q-Intersection Numbers

期刊

GEOMETRIC AND FUNCTIONAL ANALYSIS
卷 22, 期 2, 页码 443-477

出版社

SPRINGER BASEL AG
DOI: 10.1007/s00039-012-0159-6

关键词

Equivariant; Lagrangian; Fukaya category; mirror symmetry

资金

  1. NSF [DMS-0652620, DMS-0703722]
  2. ISF [1321/09]
  3. Marie Curie grant [239381]

向作者/读者索取更多资源

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 -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.

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