By Ralf Meyer
Periodic cyclic homology is a homology idea for non-commutative algebras that performs an identical function in non-commutative geometry as de Rham cohomology for soft manifolds. whereas it produces sturdy effects for algebras of soft or polynomial services, it fails for larger algebras equivalent to such a lot Banach algebras or C*-algebras. Analytic and native cyclic homology are versions of periodic cyclic homology that paintings greater for such algebras. during this e-book, the writer develops and compares those theories, emphasizing their homological homes. This contains the excision theorem, invariance less 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 practical research in bornological vector areas, that's provided within the first chapters. The focal issues listed below are the connection with inductive platforms and the useful calculus in non-commutative bornological algebras. a few chapters are extra undemanding and self sufficient of the remainder of the e-book and may be of curiosity to researchers and scholars engaged on practical research and its functions.
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