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Maurer-Cartan moduli and theorems of Riemann-Hilbert type

Research output: Contribution to journalJournal articlepeer-review

E-pub ahead of print
<mark>Journal publication date</mark>6/02/2021
<mark>Journal</mark>Applied Categorical Structures
Number of pages44
Publication StatusE-pub ahead of print
Early online date6/02/21
<mark>Original language</mark>English

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.