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Models for classifying spaces and derived deformation theory

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>2014
<mark>Journal</mark>Proceedings of the London Mathematical Society
Issue number1
Volume109
Number of pages25
Pages (from-to)40-64
Publication StatusPublished
Early online date4/02/14
<mark>Original language</mark>English

Abstract

Using the theory of extensions of L∞L∞L∞ 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∞L∞L∞ algebras and show that they possess, along with the Gerstenhaber bracket, an L∞L∞L∞ structure that is homotopy abelian.