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Cohomology theories for homotopy algebras and noncommutative geometry

Research output: Contribution to journalJournal article

Published

Journal publication date2009
JournalAlgebraic and Geometric Topology
Journal number3
Volume9
Number of pages81
Pages1503-1583
Original languageEnglish

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.