## 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 T_{ϕ} associated to a Weinstein domain M, and an exact, com-pactly supported symplectomorphism ϕ. The symplectic manifold T_{ϕ} is another Weinstein domain and its contact boundary is independent of ϕ. We distinguish T_{ϕ} from T_{1M}, 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 M_{ϕ} for the wrapped Fukaya category W.T_{ϕ} /, and we have distinguished M_{ϕ} from the mapping torus category of the identity. We prove W.T_{ϕ} / and M_{ϕ} 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 language | English (US) |
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Pages (from-to) | 1551-1630 |

Number of pages | 80 |

Journal | Geometry and Topology |

Volume | 25 |

Issue number | 3 |

DOIs | |

State | Published - 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