Maurer-Cartan moduli and theorems of Riemann-Hilbert type

23 Sep 2020 Chuang Joseph Holstein Julian Lazarev Andrey

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... (read more)

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Categories


  • ALGEBRAIC TOPOLOGY
  • CATEGORY THEORY
  • QUANTUM ALGEBRA