Distinguishing open symplectic mapping tori via their wrapped fukaya categories

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present partial results towards a classification of symplectic mapping tori using dynamical properties of wrapped Fukaya categories. More precisely, we construct a symplectic manifold Tϕ associated to a Weinstein domain M, and an exact, com-pactly supported symplectomorphism ϕ. The symplectic manifold Tϕ is another Weinstein domain and its contact boundary is independent of ϕ. We distinguish Tϕ from T1M, under certain assumptions (Theorem 1.1). As an application, we obtain pairs of diffeomorphic Weinstein domains with the same contact boundary and whose symplectic cohomology groups are the same, as vector spaces, but that are different as Liouville domains. To our knowledge, this is the first example of such pairs that can be distinguished by their wrapped Fukaya category. Previously, we have suggested a categorical model Mϕ for the wrapped Fukaya category W.Tϕ /, and we have distinguished Mϕ from the mapping torus category of the identity. We prove W.Tϕ / and Mϕ are derived equivalent (Theorem 1.9); hence, deducing the promised Theorem 1.1. Theorem 1.9 is of independent interest as it preludes an algebraic description of wrapped Fukaya categories of locally trivial symplectic fibrations as twisted tensor products.

Original languageEnglish (US)
Pages (from-to)1551-1630
Number of pages80
JournalGeometry and Topology
Volume25
Issue number3
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Floer homology on infinite-type Liouville domains
  • Fukaya categories of symplectic fibrations
  • Mapping torus category
  • Symplectic mapping torus
  • Twisted Künneth theorem
  • Twisted tensor products
  • Wrapped Fukaya category

Fingerprint

Dive into the research topics of 'Distinguishing open symplectic mapping tori via their wrapped fukaya categories'. Together they form a unique fingerprint.

Cite this