Moduli theory associated to Hochschild pairs

2021/04/07 by Iwanari, Isamu · 1 citation
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.02919

Abstract

We consider an A-linear stable infinity-category C and the pair (HH^\bullet(C/A),HH_\bullet(C/A)) of the Hochschild cohomology spectrum (Hochschild cochain complex) and the Hochschild homology spectrum (Hochschild chain complex). The purpose of this paper is to provide a moduli-theoretic interpretation of the algebraic structure on the Hochschild pair of C. The algebraic structure on the Hochschild pair is encoded by means of a two-colored topological operad called Kontsevich-Soibelman operad. The notions of cyclic deformations and equivariant deformations (of the Hochschild chain complex) associated to deformations of C play a central role.

Cited by

• Hochschild cohomology and deformation theory of stable infinity-categories with t-structures

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