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

Matilde Marcolli·Varghese Mathai
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Abstract

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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Matilde Marcolli, Varghese Mathai. 1999-11-15. Twisted index theory on good orbifolds, I: noncommutative Bloch theory. https://arxiv.org/abs/math/9911102

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