Maurer-Cartan moduli and theorems of Riemann-Hilbert type

Lazarev, Andrey and Chuang, Joseph and Holstein, Julian (2021) Maurer-Cartan moduli and theorems of Riemann-Hilbert type. Applied Categorical Structures.

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Abstract

We study Maurer–Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in several different contexts, Schlessinger–Stasheff type theorems comparing the notions of homotopy and gauge equivalence for Maurer–Cartan elements as well as their categorified versions. As an application, we re-prove and generalize Block–Smith’s higher Riemann–Hilbert correspondence, and develop its analogue for simplicial complexes and topological spaces.

Item Type:
Journal Article
Journal or Publication Title:
Applied Categorical Structures
ID Code:
151114
Deposited By:
Deposited On:
28 Jan 2021 09:40
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Sep 2021 08:12