Models for classifying spaces and derived deformation theory

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.

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

References in corpus (3)

• Deformation theory and rational homotopy type
• Cohomology theories for homotopy algebras and noncommutative geometry
• L-infinity maps and twistings