Operator Algebra Seminars

Seminar information archive ~03/04Next seminarFuture seminars 03/05~

Date, time & place Wednesday 16:30 - 18:00 122Room #122 (Graduate School of Math. Sci. Bldg.)


10:30-12:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Pedram Hekmati (Univ. Adelaide)
Dirac families and 1-cocycles (ENGLISH)
[ Abstract ]
Families of Dirac type operators, transforming covariantly under the projective action of the loop group $LG$, determine a class in twisted K-theory on compact Lie groups $G$. The loop group is the gauge group of a principal $G$-bundle over the circle and an interesting problem is to try to generalise the circle to a higher dimensional compact manifold. This is far from obvious and some of the difficulties can be modelled in a slightly simpler setting, by replacing $LG$ and gauge connections by objects which have only small differentiability in the Sobolev sense. In this talk, I will provide some background to this problem and explain how 1-cocycles naturally appear in this construction.