{"product_id":"9783540619864","title":"Asymptotic Cyclic Cohomology (Lecture Notes in Mathematics)","description":"\u003cp\u003eThe 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.\u003c\/p\u003e","brand":"Springer Verlag","offers":[{"title":"Default Title","offer_id":48761978061035,"sku":"00000_00000_00000_00000","price":128.09,"currency_code":"SGD","in_stock":true}],"url":"https:\/\/kinokuniya.com.sg\/ja\/products\/9783540619864","provider":"Books Kinokuniya Singapore","version":"1.0","type":"link"}