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 |

SUMMARY

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

CONTENT

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

Mathematics
Category theory (Mathematics)
Homological algebra
K-theory
Operator theory
Algebraic topology
Mathematics
Category Theory Homological Algebra
Algebraic Topology
K-Theory
Operator Theory