Witten deformation and the equivariant index

Details Witten deformation and the equivariant index Witten deformation and the equivariant index

2006-10-04

arxiv.org/abs/math/0610160v2

Ann. Global Anal. Geom. 34 (2008), no. 3, pp. 301--327

Mathematics

Differential Geometry

26 pages, mistakes corrected, examples added

Scientific paper

Let $M$ be a compact Riemannian manifold endowed with an isometric action of a compact Lie group. The method of the Witten deformation is used to compute the virtual representation-valued equivariant index of a transversally elliptic, first order differential operator on $M$. The multiplicities of irreducible representations in the index are expressed in terms of local quantities associated to the isolated singular points of an equivariant bundle map that is locally Clifford multiplication by a Killing vector field near these points.

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