Cyclic formality and index theorems

Dmitry Tamarkin; Boris Tsygan

doi:10.1023/A:1010838604927

Cyclic formality and index theorems

Dmitry Tamarkin^*, Boris Tsygan

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

26 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 language	English (US)
Pages (from-to)	85-97
Number of pages	13
Journal	Letters in Mathematical Physics
Volume	56
Issue number	2
DOIs	https://doi.org/10.1023/A:1010838604927
State	Published - May 2001

Funding

*Both authors are partially supported by NSF grants.

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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10.1023/A:1010838604927

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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.",

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author = "Dmitry Tamarkin and Boris Tsygan",

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language = "English (US)",

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AU - Tamarkin, Dmitry

AU - Tsygan, Boris

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N2 - 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.

AB - 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.

KW - Cyclic homology

KW - Formality theorem

KW - Hochschild (co)homology

KW - Index theorems

KW - Operad

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JF - Letters in Mathematical Physics

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ER -

Cyclic formality and index theorems

Abstract

Funding

Keywords

ASJC Scopus subject areas

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