Shyamoli Chaudhuri Plassmann, Committee Member John Roe, Committee Member Paul Frank Baum, Committee Member Nigel David Higson, Committee Chair/Co-Chair
We construct a new bivariant theory,
that we call KE-theory, which is intermediate
between the KK-theory of Gennadi Kasparov, and
the E-theory of Alain Connes and Nigel Higson.
It has an associative product, and there are
natural transformations from KK-theory into
KE-theory, and from KE-theory into E-theory which
preserve the product structures of the three
theories. We obtain in this way an explicit
description of the map between KK-theory and
E-theory, abstractly known to exist due to their
characterization using category theory.
In an effort to further elucidate the
relationship with the other two bivariant
theories, we study some of the functoriality
properties of the KE-theory groups and of the
product. The thesis concludes with an example:
we show that the new theory recovers ordinary
K-theory. All the C*-algebras that we consider
are separable, graded, and admit an action of a
locally compact sigma-compact Hausdorff group.
The thesis adviser was Prof. Nigel Higson.
