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Type: Journal article
Title: Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
Author: Kordyukov, Y.
Varghese, M.
Shubin, M.
Citation: Journal fur die Reine und Angewandte Mathematik, 2005; 581(581):193-236
Publisher: Walter de Gruyter & Co
Issue Date: 2005
ISSN: 0075-4102
Statement of
Peter Bouwknegt, Keith Hannabuss and Varghese Mathai
Abstract: In this paper, we study a refined L2 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 ╬╝ 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.
RMID: 0020050389
DOI: 10.1515/crll.2005.2005.581.193
Published version:
Appears in Collections:Pure Mathematics publications

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