Maurer–Cartan Moduli and Theorems of Riemann–Hilbert Type
Keyword(s):
Type A
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AbstractWe 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.
2012 ◽
Vol DMTCS Proceedings vol. AR,...
(Proceedings)
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1960 ◽
Vol 255
(1282)
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pp. 331-366
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Keyword(s):
1993 ◽
Vol 114
(1)
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pp. 163-189
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Keyword(s):
1999 ◽
Vol 08
(01)
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pp. 99-114
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2004 ◽
Vol 56
(6)
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pp. 1228-1236
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