Mapping tori of A∞-autoequivalences and Legendrian lifts of exact Lagrangians in circular contactizations
Year: 2025
Type: article
Abstract: We study mapping tori of quasi-autoequivalences $τ: \mathcal{A} \to \mathcal{A}$ which induce a free action of $\mathbf{Z}$ 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 $\mathcal{A}$ is directed and there is a bimodule map $\mathcal{A} (-, -) \to \mathcal{A} (-, τ(-))$ 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.
Source: Algebraic & Geometric Topology
Author: Adrian Petr
Institution: University of Southern Denmark
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4408902891