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 Mϕ-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 Mϕ, uniquely characterize it and using this, we distinguish Mϕ from the mapping torus category of the identity. The proof of the equivalence of Mϕ with wrapped Fukaya category is proven in a different paper ([17]).
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