Perturbations of Dirac operators

Perturbations of Equivariant Dirac Operators

Let M be a compact Riemannian manifold with an action by isometries of a compact Lie group G. Suppose that this action could be lifted to an action by isometries on a Clifford bundle E over M. We use the method of the Witten deformation to compute the virtual representation-valued index of a transversally elliptic Dirac operator on E. We express the multiplicities of the associated representati...

0 A ug 2 00 5 PERTURBATIONS OF DIRAC OPERATORS

We study general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the bundle endomorphism Z in the semi-classical limit s → ∞. 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...

Dirac Operators

Functional Calculus of Dirac Operators and Complex Perturbations of Neumann and Dirichlet Problems

We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in L2 for small complex L∞ perturbations of a coefficient matrix which is either real symmetric, of block form or constant. All matrices are assumed to be independent of the transversal coordinate. We solve the Neumann, Dirichlet and regularity problems through a ...

Perturbations of Operators, Ii