A Riemann-Roch-Hirzebruch formula for traces of differential operators

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Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, for the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators in a formal neighbourhood of a point. If D is the identity, the formula reduces to the Riemann--Roch--Hirzebruch formula.
31 pages, 1 figure. Misprints corrected and appendix with analytical details added in v3

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Quantum Algebra, Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/154599

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702461
 http://arxiv.org/abs/math/0702461

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arXiv