By Michael Puschnigg
The purpose of cyclic cohomology theories is the approximation of K-theory through cohomology theories outlined by way of ordinary chain complexes. the elemental instance is the approximation of topological K-theory through de Rham cohomology through the classical Chern personality. A cyclic cohomology idea for operator algebras is constructed within the booklet, in response to Connes' paintings on noncommutative geometry. Asymptotic cyclic cohomology faithfully displays the elemental houses and contours of operator K-theory. It hence turns into a typical aim for a Chern personality. The crucial results of the e-book is a basic Grothendieck-Riemann-Roch theorem in noncommutative geometry with values in asymptotic cyclic homology. in addition to this, the booklet includes a number of examples and calculations of asymptotic cyclic cohomology teams.
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