Mathematics – Differential Geometry
Scientific paper
2003-05-13
J. Reine Angew. Math. (Crelle Journal), vol. 581 (2005) 193-236.
Mathematics
Differential Geometry
41 pages, latex2e, uses xypic package. Minor clarifications made, some references added. Final version
Scientific paper
10.1515/crll.2005.2005.581.193
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 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.
Kordyukov Yuri
Mathai Varghese
Shubin Mikhail
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