Cohomology theories for homotopy algebras and noncommutative geometry

Hamilton, Alastair and Lazarev, Andrey (2009) Cohomology theories for homotopy algebras and noncommutative geometry. Algebraic and Geometric Topology, 9 (3). pp. 1503-1583. ISSN 1472-2747

Abstract

This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and L∞–algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of C∞–algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber–Schack.