Bivariante $K$-Theorie für lokalkonvexe Algebren und der Chern-Connes-Charakter

We present a new construction of a bivariant $K$-functor. The functor can be defined on various categories of topological algebras. The corresponding bivariant theory has a Kasparov product and the other standard properties of $KK$-theory. We study such a theory in detail on a natural category of locally convex algebras and define a bivariant multiplicative character to bivariant periodic cyclic cohomology.

1991 Mathematics Subject Classification:18G60, 19K35, 19L10, 46H20, 46L87

Keywords and phrases: bivariant, bivariant K-theory, bivariant Chern character, Chern-Connes-character, locally convex algebra, Frechet algebra, extension, K-theory for topological algebras, cyclic homology for topological algebras

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