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arXiv · 1209.3866

Models for classifying spaces and derived deformation theory

Andrey Lazarev
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Abstract

Using the theory of extensions of L-infinity algebras, we construct rational homotopy models for classifying spaces of fibrations, giving answers in terms of classical homological functors, namely the Chevalley-Eilenberg and Harrison cohomology. We also investigate the algebraic structure of the Chevalley-Eilenberg complexes of L-infinity algebras and show that they possess, along with the Gerstenhaber bracket, an L-infinity structure that is homotopy abelian.

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Andrey Lazarev. 2012-09-18. Models for classifying spaces and derived deformation theory. https://arxiv.org/abs/1209.3866

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