Birational Calabi-Yau manifolds have the same small quantum products

Abstract

We show that any two birational projective Calabi-Yau manifolds have isomorphic small quantum cohomology algebras after a certain change of Novikov rings. The key tool used is a version of an algebra called symplectic cohomology, which is constructed using Hamiltonian Floer cohomology. Morally, the idea of the proof is to show that both small quantum products are identical deformations of symplectic cohomology of some common open affine subspace.

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      author = {Kato, Kazuya},
      title = {Existence theorem for higher local fields},
      booktitle = {Invitation to Higher Local Fields},
      venue = {{M}ünster, 1999},
      series = {Geom. Topol. Monogr.},
      volume = {3},
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      publisher = {Geom. Topol. Publ., Coventry},
      year = {2000},
      mrclass = {11S70 (19D45 19F05)},
      mrnumber = {1804933},
      mrreviewer = {Jerzy Browkin},
      doi = {10.2140/gtm.2000.3.165},
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      volume = {44},
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Authors

Mark McLean

Stony Brook University, Stony Brook, NY