Author	Puschnigg, Michael. author
Title	Asymptotic Cyclic Cohomology [electronic resource] / by Michael Puschnigg
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1996
Connect to	http://dx.doi.org/10.1007/BFb0094458
Descript	XXIV, 244 p. online resource

The aim of cyclic cohomology theories is the approximation of K-theory by cohomology theories defined by natural chain complexes. The basic example is the approximation of topological K-theory by de Rham cohomology via the classical Chern character. A cyclic cohomology theory for operator algebras is developed in the book, based on Connes' work on noncommutative geometry. Asymptotic cyclic cohomology faithfully reflects the basic properties and features of operator K-theory. It thus becomes a natural target for a Chern character. The central result of the book is a general Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. Besides this, the book contains numerous examples and calculations of asymptotic cyclic cohomology groups

The asymptotic homotopy category -- Algebraic de Rham complexes -- Cyclic cohomology -- Homotopy properties of X-complexes -- The analytic X-complex -- The asymptotic X-complex -- Asymptotic cyclic cohomology of dense subalgebras -- Products -- Exact sequences -- KK-theory and asymptotic cohomology -- Examples

1. Mathematics
2. Category theory (Mathematics)
3. Homological algebra
4. K-theory
5. Operator theory
6. Algebraic topology
7. Mathematics
8. Category Theory
9. Homological Algebra
10. Algebraic Topology
11. K-Theory
12. Operator Theory