EMS Tracts in Mathematics 2007; 368 pp; hardcover Volume: 3 ISBN10: 3037190396 ISBN13: 9783037190395 List Price: US$78 Member Price: US$62.40 Order Code: EMSTM/3
 Periodic cyclic homology is a homology theory for noncommutative algebras that plays a similar role in noncommutative 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 ChernConnes 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 noncommutative bornological algebras. 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. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in local and analytic cyclic homology. Table of Contents  Bornological vector spaces and inductive systems
 Relations between entire, analytic, and local cyclic homology
 The spectral radius of bounded subsets and its applications
 Periodic cyclic homology via pronilpotent extensions
 Analytic cyclic homology and analytically nilpotent extensions
 Local homotopy invariance and isoradial subalgebras
 The ChernConnes character
 Appendix. Background material
 Bibliography
 Notation and symbols
 Index
