Perturbations of Dirac operators

[摘要] We study general conditions under which the computations of the index of a perturbed Dirac operator D-s = D + sZ localize to the singular set of the bundle endomorphism Z in the semiclassical limit s -> infinity. We show how to use Witten's method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. In particular, we provide examples of novel deformations of the de Rham operator to establish new results relating the Euler characteristic of a spin(c) manifold to maps between its even and odd spinor bundles. (c) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-31

[关键词] index;Witten deformation;perturbation;singularity;Dirac operator;localization