By Ralf Meyer
Periodic cyclic homology is a homology conception for non-commutative algebras that performs an identical function in non-commutative geometry as de Rham cohomology for tender manifolds. whereas it produces stable effects for algebras of tender or polynomial features, it fails for higher algebras corresponding to so much Banach algebras or C*-algebras. Analytic and native cyclic homology are versions of periodic cyclic homology that paintings larger for such algebras. during this publication, the writer develops and compares those theories, emphasizing their homological houses. This comprises the excision theorem, invariance lower than passage to definite dense subalgebras, a common Coefficient Theorem that relates them to $K$-theory, and the Chern-Connes personality for $K$-theory and $K$-homology. The cyclic homology theories studied during this textual content require a great deal of sensible research in bornological vector areas, that is provided within the first chapters. The focal issues listed here are the connection with inductive platforms and the practical calculus in non-commutative bornological algebras. a few chapters are extra easy and self sustaining of the remainder of the e-book and may be of curiosity to researchers and scholars engaged on practical research and its functions.