Wang, Juan: Generalized Snaith Splittings. - Bonn, 2009. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc:
author = {{Juan Wang}},
title = {Generalized Snaith Splittings},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2009,
month = feb,

note = {A Segal Γ-space A gives a homotopy functor A(X) and a connective homology theory h*(X;A) = π*(A(X)). The infinite symmetric product SP(X) and the configuration space C(R;X) ≅ Q(X) are well-known examples of Segal Γ-spaces; the former giving singular homology H*(X;Z) and the latter stable homotopy theory as their homotopy groups. Here we are concerned with another important example, the Segal Γ-space K leading to connective KO-theory: π*K(X) = ̃ko(X).
Like the first two examples, such functors A come very often with a filtration An(X) which splits after applying another suitable homotopy functor, perhaps even a Segal Γ-space B; in the first two examples one can take B = A and obtain the well-known Dold-Puppe splitting of SP(X) resp. the Snaith splitting of Q(X). Our main result is a splitting of K(X) using the functor B(X+) ≅ Ω∞-1(MO∧X+) representing unoriented cobordism, namely

B(K(X)+) ≅ B(V n=o Kn(X)/Kn-1(X)).


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