Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 348

The spectrum of periodic point perturbations and the Krein resolvent formula

J. Brüning and V. A. Geyler

We study periodic point perturbations, H, of a periodic elliptic operator H0 on a connected complete non-compact Riemannian manifold X, endowed with an isometric, effective, properly discontinuous, and co-compact action of a discrete group Gamma. Under some conditions on H0, we prove that the gaps of the spectrum are labelled in a natural way by elements of the K0-group of a certain C*-algebra. In particular, if the group Gamma has the Kadison property then the spectrum has band structure. The Krein resolvent formula plays a crucial role in proving the main results.

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