Minimal projective extensions of compact spaces.

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, ...

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.

We compute the Grothendieck group K0 of non-commutative analogues of projective space bundles. Our results specialize to give the K0-groups of non-commutative analogues of projective spaces, and specialize to recover the K0-group of a usual projective space bundle over a regular noetherian separated scheme. As an application, we develop an intersection theory for quantum ruled surfaces.

We consider some classical maps from the theory of abelian varieties and their moduli spaces, and prove their definability on restricted domains in the o-minimal structure Ran,exp. In particular, we prove that the projective embedding of the moduli space of the principally polarized abelian variety Sp(2g,Z)\Hg is definable in Ran,exp when restricted to Siegel’s fundamental set Fg . We also prov...

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used...

A general framework for integration over certain innnite dimensional spaces is rst developed using projective limits of a projective family of compact Hausdorr spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, innnite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used eith...

We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.

Let M be one of the projective spaces CP, HP for n ≥ 2 or the Cayley projective plane OP2, and let ΛM denote the free loop space on M . Using Morse theory methods, we prove that the suspension spectrum of (ΛM)+ is homotopy equivalent to the suspension spectrum of M+ wedge a family of Thom spaces of explicit vector bundles over the tangent sphere bundle of M . MSC: 55P42; 58E05; 53C35; 55P35

We show that the family of spectral triples for quantum projective spaces introduced by D’Andrea and Da̧browski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2ρ or its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connecti...