Daniel Stevenson, UCR

Title: `Cyclic homology and the twisted Chern character'

Abstract: The twisted K-theory of a manifold M is defined as vertical
homotopy classes of sections of a bundle with fibre the Fredholm operators
of some complex Hilbert space or alternatively as the K-theory of the
C^*-algebra of sections of a bundle of infinite dimensional matrix
algebras over M.  One difference from ordinary K-theory is that the target
space of the Chern character is a `twisted' version of de Rham cohomology.
We give a construction of this Chern character in the spirit of
non-commutative geometry by identifying the periodic cyclic homology of a
smooth sub-algebra of the C^* algebra with twisted de Rham cohomology.
This is joint work with Mathai Varghese from University of Adelaide.