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Nest, Ryszard; Tsygan, Boris

Algebraic index theorem. (English) Zbl 0887.58050

Commun. Math. Phys. 172, No. 2, 223-262 (1995).
This paper is the first in a series aimed at providing an algebraic insight to various Atiyah-Singer type index theorems: We prove the Atiyah-Singer index theorem where the algebra of pseudo-differential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold.

Cited in 7 Reviews
Cited in 77 Documents

MSC:

58J20 Index theory and related fixed-point theorems on manifolds
53D55 Deformation quantization, star products

Keywords:

Atiyah-Singer index theorem; deformation quantization; algebra of functions on a symplectic manifold
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\textit{R. Nest} and \textit{B. Tsygan}, Commun. Math. Phys. 172, No. 2, 223--262 (1995; Zbl 0887.58050)
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