Locality of relative symplectic cohomology for complete embeddings

Yoel Groman, Umut Varolgunes

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

A complete embedding is a symplectic embedding of a geometrically bounded symplectic manifold into another geometrically bounded symplectic manifold of the same dimension. When satisfies an additional finiteness hypothesis, we prove that the truncated relative symplectic cohomology of a compact subset inside is naturally isomorphic to that of its image inside. Under the assumption that the torsion exponents of are bounded, we deduce the same result for relative symplectic cohomology. We introduce a technique for constructing complete embeddings using what we refer to as integrable anti-surgery. We apply these to study symplectic topology and mirror symmetry of symplectic cluster manifolds and other examples of symplectic manifolds with singular Lagrangian torus fibrations satisfying certain completeness conditions.

Original languageAmerican English
Pages (from-to)2551-2637
Number of pages87
JournalCompositio Mathematica
Volume159
Issue number12
DOIs
StatePublished - 10 Oct 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s).

Keywords

  • Floer theory
  • cluster manifolds
  • integrable systems
  • symplectic cohomology

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