Dynamical invariants of mapping torus categories

Yusuf Barış Kartal

doi:10.1016/j.aim.2021.107882

Dynamical invariants of mapping torus categories

Yusuf Barış Kartal

Mathematics

Research output: Contribution to journal › Article › peer-review

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)
Article number	107882
Journal	Advances in Mathematics
Volume	389
DOIs	https://doi.org/10.1016/j.aim.2021.107882
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

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10.1016/j.aim.2021.107882

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title = "Dynamical invariants of mapping torus categories",

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]).",

keywords = "Categorical dynamics, Flux group, Homological mirror symmetry, Mapping torus, Noncommutative geometry",

author = "Kartal, {Yusuf Barı{\c s}}",

note = "Funding Information: I would like to first thank to my advisor Paul Seidel, who introduced me to this problem and without his guidance this work would not be possible. I would also like to thank Padmavathi Srinivasan for illuminating conversations on the Tate curve and Neron models, to Yankı Lekili for conversations on their work [22] and [23] and to Dhruv Ranganathan for conversations on the Tate curve as a rigid model for . Finally, I would like to thank the referee for reading the paper, and useful suggestions. This work was partially supported by NSF grant DMS-1500954 and by the Simons Foundation (through a Simons Investigator award, award no. 256290 ). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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doi = "10.1016/j.aim.2021.107882",

language = "English (US)",

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N1 - Funding Information: I would like to first thank to my advisor Paul Seidel, who introduced me to this problem and without his guidance this work would not be possible. I would also like to thank Padmavathi Srinivasan for illuminating conversations on the Tate curve and Neron models, to Yankı Lekili for conversations on their work [22] and [23] and to Dhruv Ranganathan for conversations on the Tate curve as a rigid model for . Finally, I would like to thank the referee for reading the paper, and useful suggestions. This work was partially supported by NSF grant DMS-1500954 and by the Simons Foundation (through a Simons Investigator award, award no. 256290 ). Publisher Copyright: © 2021 Elsevier Inc.

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N2 - 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]).

AB - 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]).

KW - Categorical dynamics

KW - Flux group

KW - Homological mirror symmetry

KW - Mapping torus

KW - Noncommutative geometry

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Dynamical invariants of mapping torus categories

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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