Institut de Mathématiques de Luminy

Abstract 2002-11

Puschnigg Michael.
Homology functors of ind-algebras and local cyclic cohomology I.

A central topic of noncommutative geometry id the study of topological algebras by means of homology theories. The most important of these theories (and most elementary in terms of its definition) is topological K-theory. K-theory is a covariant functor on any category of topological algebras. A for which the invertible elements of the unitalization à form an open set. Its essential properties apart from excision, which will not be considered in this paper, are :

  • Invariance with respect to continuous homotopies

  • Invariance under infinitesimal deformations

  • Stability under passage to dense subalgebras which are closed under holomorphic functional calculus

  • Compatibility with topological limits

  • Stability under tensorization with matrix algebras, under projective tensor products with operator ideals and C*-tensor products with the algebra of compact operators on a Hilbert space.

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Last update : june 21, 2002, EL.