A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras

2014/07/24 by Dolgushev, Vasily A., Rogers, Christopher L.
#Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1407.6735

Abstract

In this paper we consider L_∞-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an L_∞ quasi-isomorphism U: L → L induces a weak equivalence between the Deligne-Getzler-Hinich (DGH) ∞-groupoids corresponding to L and L, respectively. This paper may be considered as a modest addition to foundational paper arXiv:math/0404003 by Ezra Getzler.

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