Dynamical invariants of mapping torus categories

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 $M_{\varphi }$-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 $M_{\varphi }$, uniquely characterize it and using this, we distinguish $M_{\varphi }$ from the mapping torus category of the identity. The proof of the equivalence of $M_{\varphi }$ with wrapped Fukaya category is proven in a different paper (arXiv:1907.01156).