Mapping tori of A∞-autoequivalences and Legendrian lifts of exact Lagrangians in circular contactizations

Petr, Adrian

doi:10.2140/agt.2025.25.489

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Mapping tori of $A_{\infty}$-autoequivalences and Legendrian lifts of exact Lagrangians in circular contactizations

Adrian Petr

Algebraic & Geometric Topology 25 (2025) 489–561

DOI: 10.2140/agt.2025.25.489

Abstract

We study mapping tori of quasi-autoequivalences $τ : 𝒜 \to 𝒜$ which induce a free action of $ℤ$ on objects. More precisely, we compute the mapping torus of $τ$ when it is strict and acts bijectively on hom-sets, or when the $A_{\infty}$ -category $𝒜$ is directed and there is a bimodule map $𝒜 (-, -) \to 𝒜 (-, τ (-))$ satisfying some hypotheses. Then we apply these results in order to link together the Fukaya $A_{\infty}$ -category of a family of exact Lagrangians, and the Chekanov–Eliashberg DG-category of Legendrian lifts in the circular contactization.

Keywords

Fukaya categories, Legendrian contact homology, group action on $A_{\infty}$-categories

Mathematical Subject Classification

Primary: 53D42, 53D37, 18G70

References

Publication

Received: 15 December 2022

Revised: 24 August 2023

Accepted: 15 November 2023

Published: 24 March 2025

Authors

Adrian Petr
Center for Quantum Mathematics University of Southern Denmark (SDU) Odense Denmark

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Volume 25, issue 1 (2025)