Cyclic formality and index theorems

Dmitry Tamarkin*, Boris Tsygan

*Corresponding author for this work

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

The Letter announces the following results (the proofs will appear elsewhere). An operad actine on Hochschild chains and cochains of an associative algebra is constructed. This operad is formal. In the case when this algebra is the algebra of smooth function on a smooth manifold, the action of this operad on the corresponding Hochschild chains and cochains is formal. The induced map on the (periodic) cyclic homology is given by the formula involving the A-genus. The index theorem for degenerate Poisson structures follows from the latter fact.

Original languageEnglish (US)
Pages (from-to)85-97
Number of pages13
JournalLetters in Mathematical Physics
Volume56
Issue number2
DOIs
StatePublished - May 1 2001

Keywords

  • Cyclic homology
  • Formality theorem
  • Hochschild (co)homology
  • Index theorems
  • Operad

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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