Models for classifying spaces and derived deformation theory

2012/09/18 by Lazarev, Andrey
#Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1209.3866

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.

Related

• L-infinity maps and twistings
• E-infinity structures over L-algebras
• The integration theory of curved absolute L-infinity algebras
• Maurer-Cartan moduli and models for function spaces
• Infinity Algebras, Cohomology and Cyclic Cohomology, and Infinitesimal Deformations