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

Vasily A. Dolgushev; Christopher L. Rogers

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

Algebraic Topology 2015-03-10 v2 Quantum Algebra

Authors: Vasily A. Dolgushev , Christopher L. Rogers

Abstract

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

Keywords

l-infinity algebras goldman-millson theorem filtered algebras deligne-getzler-hinich groupoids weak equivalence quasi-isomorphism

Cite

@article{arxiv.1407.6735,
  title  = {A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras},
  author = {Vasily A. Dolgushev and Christopher L. Rogers},
  journal= {arXiv preprint arXiv:1407.6735},
  year   = {2015}
}

Comments

The final version will appear in the Journal of Algebra. Comments are still welcome

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

Abstract

Keywords

Cite

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