Local and analytic cyclic homology
By: Ralf Meyer
Series: EMS tracts in mathematics -- 3
Publisher: European Mathematical Society
Published: 2007
Place of publication: Zürich
Language: eng
Number of pages: 360
ISBN-13: 9783037190395
Subjects: Algebra, Homological; Homology theory; Banach algebras
Description: "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, emphasizing 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." "This 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 on functional analysis and its applications."--BOOK JACKET.
Notes: Includes bibliographical references (p. [343]-348) and index