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

Petr, Adrian¹

¹Center for Quantum Mathematics, University of Southern Denmark (SDU), Odense, Denmark

Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 489-561

Résumé

We study mapping tori of quasi-autoequivalences τ : 𝒜→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∞-category 𝒜 is directed and there is a bimodule map 𝒜(−, −) →𝒜(−,τ(−)) satisfying some hypotheses. Then we apply these results in order to link together the Fukaya A∞-category of a family of exact Lagrangians, and the Chekanov–Eliashberg DG-category of Legendrian lifts in the circular contactization.

Détail

DOI : 10.2140/agt.2025.25.489

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

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