Geodesic
Diffeotopy functors of ind-algebras and local cyclic cohomology
Documenta mathematica, Tome 8 (2003), pp. 143-245.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We introduce a new bivariant cyclic theory for topological algebras, called local cyclic cohomology. It is obtained from bivariant periodic cyclic cohomology by an appropriate modification, which turns it into a deformation invariant bifunctor on the stable diffeotopy category of topological ind-algebras. We set up homological tools which allow the explicit calculation of local cyclic cohomology. The theory turns out to be well behaved for Banach- and $C^*$-algebras and possesses many similarities with Kasparov's bivariant operator K-theory. In particular, there exists a multiplicative bivariant Chern-Connes character from bivariant K-theory to bivariant local cyclic cohomology.
Classification : 46L80, 46L85, 18G60, 18E35, 46M99
Keywords: topological ind-algebra, infinitesimal deformation, almost multiplicative map, stable diffeotopy category, Fréchet algebra, Banach algebra, bivariant cyclic cohomology, local cyclic cohomology, bivariant Chern-connes character 
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     author = {Puschnigg, Michael},
     title = {Diffeotopy functors of ind-algebras and local cyclic cohomology},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a10/}
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Puschnigg, Michael. Diffeotopy functors of ind-algebras and local cyclic cohomology. Documenta mathematica, Tome 8 (2003), pp. 143-245. http://geodesic.mathdoc.fr/item/DOCMA_2003__8__a10/