# Book Details

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Preface | Table of Contents | Introduction | MARC record | Metadata XML | e-Book PDF (2715 KB)*Ralf Meyer (University of GĂ¶ttingen, Germany)*

#### Local and Analytic Cyclic Homology

ISBN print 978-3-03719-039-5, ISBN online 978-3-03719-539-0DOI 10.4171/039

August 2007, 368 pages, hardcover, 17.0 x 24.0 cm.

58.00 Euro

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 Chernâ€“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.

*Keywords: *Cyclic homology, bornology, Banach algebra, non-commutative geometry, functional calculus, K-theory

#### Further Information

Review in Zentralblatt MATH 1134.46001