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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory

Y. Kordyukov1 / V. Mathai2 / M. Shubin3

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Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 581, Pages 193–236, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.581.193, July 2005

Publication History

Received:
27. Mai 2003
Revised:
26. April 2004
Published Online:
2005-07-27

Abstract

In this paper, we study a refined L 2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral projections (and not just their traces) and obtain information about classes of these projections in K-theory in the semiclassical limit as the coupling constant μ goes to zero. An important corollary is a vanishing theorem for the higher traces in cyclic cohomology for the spectral projections. This result is then applied to the quantum Hall effect. We also give a new proof that there are arbitrarily many gaps in the spectrum of the operators under consideration in the semiclassical limit.

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