### Analytic cyclic cohomology, by Ralf Meyer

We prove excision in entire and periodic cyclic cohomology and
construct a Chern-Connes character for Fredholm modules over a
C*-algebra without summability restrictions, taking values in a
variant of Connes's entire cyclic cohomology.

Before these results can be obtained, we have to sort out some
fundamental questions about the class of algebras on which to define
entire cyclic cohomology. The right domain of definition for entire
cyclic cohomology is the category of complete bornological algebras.
For these algebras, we define a bivariant cohomology theory, called
analytic cyclic cohomology, that contains Connes's entire cyclic
cohomology as a special case.

The definition of analytic cyclic cohomology is based on the
Cuntz-Quillen approach to cyclic cohomology theories using tensor
algebras and X-complexes. The appropriate completion of the tensor
algebra that yields analytic cyclic cohomology can be understood using
an appropriate notion of analytic nilpotence.

In addition, we develop the elementary theory of analytic cyclic
cohomology (smooth homotopy invariance, stability, Chern character in
K-theory).

This is the author's thesis, written under the supervision of Joachim
Cuntz at the Universitaet Muenster.

Ralf Meyer <rameyer@math.uni-muenster.de>