By Michael Puschnigg
The purpose of cyclic cohomology theories is the approximation of K-theory via cohomology theories outlined via average chain complexes. the elemental instance is the approximation of topological K-theory via de Rham cohomology through the classical Chern personality. A cyclic cohomology thought for operator algebras is constructed within the booklet, according to Connes' paintings on noncommutative geometry. Asymptotic cyclic cohomology faithfully displays the elemental homes and contours of operator K-theory. It hence turns into a traditional goal for a Chern personality. The important results of the e-book is a basic Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. along with this, the ebook includes a number of examples and calculations of asymptotic cyclic cohomology teams.
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