Integral Excision for K-Theory

Details Integral Excision for K-Theory Integral Excision for K-Theory

2010-09-15

arxiv.org/abs/1009.3044v1

Mathematics

Algebraic Topology

21 pages

Scientific paper

If A is a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, then the cube induced by Goodwillie's integral cyclotomic trace from K(A) to TC(A) is homotopy cartesian. In other words, the homotopy fiber of the cyclotomic trace satisfies excision. The method of proof gives as a spin-off new proofs of some old results, as well as some new results, about periodic cyclic homology, and - more relevantly for our current application - the T-Tate spectrum of topological Hochschild homology, where T is the circle group

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