M.Sc. Eric Schlarmann (16.15 - 16.45)

A smooth model for the classifying space of equivariant K-theory.

Abstract: Complex K-theory is classified by the space of Fredholm operators, by
the Atiyah-Jänich theorem. It is known that one can up to homotopy pass
to a more structured space of operators, known as the restricted general
linear group. This is an infinite dimensional manifold with a Lie group
structure, for which the universal Chern character classes can be
represented as invariant differential forms. I will show that one can
also make this transition in the equivariant setting and obtain explicit
differential form representatives for the equivariant Chern character in
a suitable equivariant cohomology theory.