Twisted index theory on good orbifolds, I: noncommutative Bloch theory

Details Twisted index theory on good orbifolds, I: noncommutative Bloch theory Twisted index theory on good orbifolds, I: noncommutative Bloch theory

1999-11-15

arxiv.org/abs/math/9911102v1

Communications in Contemporary Mathematics, Vol. 1, N. 4 (1999) 553-587

Mathematics

Differential Geometry

34 pages, LaTex

Scientific paper

This paper, together with Part II, expands the results of math.DG/9803051. In Part I we study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in 2 and 4 dimensions, related to generalizations of the Bethe-Sommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.

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