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

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dc.creatorKordyukov, Y.
dc.creatorMathai, V.
dc.creatorShubin, M.
dc.date2003-05-13
dc.date2004-04-26
dc.date.accessioned2026-07-07T06:21:37Z
dc.date.available2026-07-07T06:21:37Z
dc.descriptionIn 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 an 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.
dc.description41 pages, latex2e, uses xypic package. Minor clarifications made, some references added. Final version
dc.identifierhttps://arxiv.org/abs/math/0305189
dc.identifierhttp://arxiv.org/abs/math/0305189
dc.identifierJ. Reine Angew. Math. (Crelle Journal), vol. 581 (2005) 193-236.
dc.identifierdoi:10.1515/crll.2005.2005.581.193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95651
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subjectK-Theory and Homology
dc.subjectSpectral Theory
dc.subject46L80, 58J37, 58J50
dc.titleEquivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory
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