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[null,"1.","Record Nr.",null,"UNINA9910151936103321"]
[null,null,"Autore",null,"Meyer Ralf"]
[null,null,"Titolo",null,"Local and Analytic Cyclic Homology [[electronic resource] /] / Ralf Meyer"]
[null,null,"Pubbl/distr/stampa",null,"Zuerich, Switzerland, : European Mathematical Society Publishing House, 2007"]
[null,null,"ISBN",null,"3-03719-539-8"]
[null,null,"Descrizione fisica",null,"1 online resource (368 pages)"]
[null,null,"Collana",null,"EMS Tracts in Mathematics (ETM) ; 3"]
[null,null,"Classificazione",null,"19-xx46-xx"]
[null,null,"Soggetti",null,"Algebraic geometry"]
[{"$nulls":4},"Functional analysis"]
[{"$nulls":4},"$K$-theory"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Sommario/riassunto","Periodic cyclic homology is a homology theory for non-commutative algebras  that plays a similar role in non-commutative geometry as de Rham  cohomology for smooth manifolds. While it produces good results for  algebras of smooth or polynomial functions, it fails for bigger  algebras such as most Banach algebras or C*-algebras. Analytic  and local cyclic homology are variants of periodic cyclic homology  that work better for such algebras. In this book the author  develops and compares these theories, emphasising their homological  properties. This includes the excision theorem, invariance under  passage to certain dense subalgebras, a Universal Coefficient  Theorem that relates them to K-theory, and the Chern-Connes  character for K-theory and K-homology.        The cyclic homology theories studied in this text require a good  deal of functional analysis in bornological vector spaces, which is  supplied in the first chapters. The focal points here are the  relationship with inductive systems and the functional calculus in  non-commutative bornological algebras.        The book is mainly intended for researchers and advanced graduate  students interested in non-commutative geometry. Some chapters are  more elementary and independent of the rest of the book, and will  be of interest to researchers and students working in functional  analysis and its applications."]