Wang, Juan: Generalized Snaith Splittings. - Bonn, 2009. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.

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@phdthesis{handle:20.500.11811/4031,

urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-16683,

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

Like the first two examples, such functors A come very often with a filtration A

url = {http://hdl.handle.net/20.500.11811/4031}

}

urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-16683,

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 A

_{n}(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} K_{n}(X)/K_{n-1}(X)).

url = {http://hdl.handle.net/20.500.11811/4031}

}