Box splines and the equivariant index theorem

Autor:	De Concini, C., Procesi, C., Vergne, M.
Rok vydání:	2010
Předmět:	Mathematics - Differential Geometry Mathematics - K-Theory and Homology
Druh dokumentu:	Working Paper
Popis:	In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distributions, on the dual of the group G or on the dual of its Lie algebra. The morphism from K-theory to cohomology is analyzed and the multiplication by the Todd class is shown to correspond to the operator (deconvolution) inverting the semidiscrete convolution with a box spline. Finally, the multiplicities of the index of a G-transversally elliptic operator on M are determined using the infinitesimal index of the symbol. Comment: 44 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1012.1049 Zobrazit plný text záznamu View this record from Arxiv