Index pairings and residue formulas for a noncommutative 2-sphere

Elmar Wagner (Michoacan University)

Tuesday 18th May, 2010 16:00-17:00 214


In the general framework of noncommutative geometry, residue formulas are used to associate cyclic cocycles to (regular) spectral triples and to compute index pairings. Applying these ideas to the 0-summable spectral triple on the standard Podles sphere, a noncommutative 2-sphere, one faces two problems: First, the spectral triple fails the regularity condition, which is a prerequisite for the development of a pseudo-differential calculus and the definition of "local" index formulas. Next, the Hochschild and cyclic cohomologies are in some sense degenerated - one needs twisted versions of these cohomology theories to obtain good correspondence to the classical case. To deal with these problems, we present the definition of a twisted Chern character from equivariant K_0-theory into twisted cyclic homology, give residue formulas for some distinguished (twisted) cocycles on the standard Podles sphere, and then compute the index pairing. (Joint work with Ulrich Krähmer.)

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