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arXiv · 1802.02549

Maurer-Cartan moduli and theorems of Riemann-Hilbert type

Joseph Chuang·Julian Holstein·Andrey Lazarev
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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.

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BibTeXRIS

Joseph Chuang, Julian Holstein, Andrey Lazarev. 2018-02-07. Maurer-Cartan moduli and theorems of Riemann-Hilbert type. https://arxiv.org/abs/1802.02549

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