Index pairings and residue formulas for a noncommutative 2-sphere

Elmar Wagner (Michoacan University)

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

Abstract

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.)

Add to your calendar

Download event information as iCalendar file (only this event)