Maurer-Cartan moduli and theorems of Riemann-Hilbert type

Chuang, Joseph and Holstein, Julian and Lazarev, Andrey (2021) Maurer-Cartan moduli and theorems of Riemann-Hilbert type. Applied Categorical Structures, 29 (4). pp. 685-728. ISSN 1572-9095

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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
Uncontrolled Keywords:
?? maurer-cartan elementdifferential graded algebrasimplicial complexsmooth manifoldlocally constant sheaftheoretical computer sciencecomputer science(all) ??
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Deposited On:
28 Jan 2021 09:40
Last Modified:
13 Nov 2023 00:25