The differential calculus of homotopy functors. (English) Zbl 0759.55011

Goodwillie, Thomas G.

Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 621-630 (1991).

[For the entire collection see Zbl 0741.00019.]
The paper is a short account of the talk given at the International Congress 1990. The author demonstrates how his powerful theory of calculus of functors can be applied to prove deep theorems, in this case a result on the connection of relative algebraic \(K\)-theory of spaces as defined by Waldhausen with relative topological cyclic homology as introduced by Bökstedt-Hsiang-Madsen. The reader should concentrate his attention to the methods and consider the result as a statement. Details including all assumptions necessary for a rigorous proof will appear elsewhere.

Reviewer: R.Vogt (Osnabrück)

MSC:

55P99	Homotopy theory
19D10	Algebraic \(K\)-theory of spaces

Keywords:

calculus of functors; relative algebraic \(K\)-theory; topological cyclic homology