Models for classifying spaces and derived deformation theory
Algebraic Topology
2013-12-13 v3 Quantum Algebra
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.
Cite
@article{arxiv.1209.3866,
title = {Models for classifying spaces and derived deformation theory},
author = {Andrey Lazarev},
journal= {arXiv preprint arXiv:1209.3866},
year = {2013}
}
Comments
23 pages. This version contains minor technical corrections and a new section with a list of open problems. To appear in Proceedings of the LMS