Topological cyclic homology

Abstract

Topological cyclic homology is a refinement of Connes-Tsygan's cyclic homology which was introduced by Bkstedt-Hsiang-Madsen in 1993 as an approximation to algebraic K-theory. There is a trace map from algebraic K-theory to topological cyclic homology, and a theorem of Dundas-Goodwillie-McCarthy asserts that this induces an equivalence of relative theories for nilpotent immersions, which gives a way for computing K-theory in various situations. The construction of topological cyclic homology is based on genuine equivariant homotopy theory, the use of explicit point-set models, and the elaborate notion of a cyclotomic spectrum.

Topics & Concepts