Geodesic
Diffeotopy functors of ind-algebras and local cyclic cohomology
Documenta mathematica, Tome 8 (2003), pp. 143-245
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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.
DOI : 10.4171/dm/143
Classification : 18E35, 46L80, 46L85, 46M99
Mots-clés : Banach algebra, Fréchet algebra, topological ind-algebra, infinitesimal deformation, almost multiplicative map, stable diffeotopy category, bivariant cyclic cohomology, local cyclic cohomology, bivariant Chern-connes character 
@article{10_4171_dm_143,
     author = {Michael Puschnigg},
     title = {Diffeotopy functors of ind-algebras and local cyclic cohomology},
     journal = {Documenta mathematica},
     pages = {143--245},
     year = {2003},
     volume = {8},
     doi = {10.4171/dm/143},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/143/}
}
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Michael Puschnigg. Diffeotopy functors of ind-algebras and local cyclic cohomology. Documenta mathematica, Tome 8 (2003), pp. 143-245. doi: 10.4171/dm/143

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