## Abstract

This paper describes constructions in homological algebra that are part of a strategy whose goal is to understand and classify symplectic mapping tori. More precisely, given a dg category and an auto-equivalence, satisfying certain assumptions, we introduce a category M_{ϕ}-called the mapping torus category- that describes the wrapped Fukaya category of an open symplectic mapping torus. Then we define a family of bimodules on a natural deformation of M_{ϕ}, uniquely characterize it and using this, we distinguish M_{ϕ} from the mapping torus category of the identity. The proof of the equivalence of M_{ϕ} with wrapped Fukaya category is proven in a different paper ([17]).

Original language | English (US) |
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Article number | 107882 |

Journal | Advances in Mathematics |

Volume | 389 |

DOIs | |

State | Published - Oct 8 2021 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Categorical dynamics
- Flux group
- Homological mirror symmetry
- Mapping torus
- Noncommutative geometry