Algebraic & Geometric Topology 9 (2009) 1503–1583

DOI: 10.2140/agt.2009.9.1503

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.

Keywords

infinity-algebra, cyclic cohomology, Harrison cohomology, symplectic structure, Hodge decomposition

Mathematical Subject Classification

Primary: 13D03, 13D10

Secondary: 46L87

References

Publication

Received: 2 December 2008
Revised: 31 May 2009
Accepted: 23 June 2009
Published: 1 August 2009

Authors