Corpus ID: 212747571

The quantitative nature of reduced Floer theory

  title={The quantitative nature of reduced Floer theory},
  author={S. Venkatesh},
  journal={arXiv: Symplectic Geometry},
  • S. Venkatesh
  • Published 2020
  • Mathematics
  • arXiv: Symplectic Geometry
  • We study the reduced symplectic cohomology of disk subbundles in negative symplectic line bundles. We show that this cohomology theory "sees" the spectrum of a quantum action on quantum cohomology. Precisely, quantum cohomology decomposes into generalized eigenspaces of the action of the first Chern class by quantum cup product. The reduced symplectic cohomology of a disk bundle of radius $R$ sees all eigenspaces whose eigenvalues have size less than $R$, up to rescaling by a fixed constant… CONTINUE READING

    Figures from this paper


    Mayer-Vietoris property for relative symplectic cohomology
    • 7
    • PDF
    Floer theory and reduced cohomology on open manifolds
    • 14
    • Highly Influential
    • PDF
    Completed Symplectic Cohomology and Liouville Cobordisms
    • 1
    • Highly Influential
    Fibered symplectic cohomology and the Leray-Serre spectral sequence
    • 31
    • PDF
    J-Holomorphic Curves and Symplectic Topology
    • 1,065
    • PDF
    Floer homology and Novikov rings
    • 256
    • Highly Influential
    • PDF
    Functors and Computations in Floer Homology with Applications, I
    • 326
    Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties
    • 17
    • Highly Influential
    • PDF
    Symplectic cohomology and Viterbo's theorem
    • 77
    • PDF
    Birational Calabi-Yau manifolds have the same small quantum products
    • 5
    • PDF