Let G be a finite p-group, p ≠ 2. We construct a map from the space JG, defined as the fiber of ψk-1: BGO → BGSpin, to the space (SFG)p, defined as the 1-component of the zeroth space of the equivariant p-complete sphere spectrum. Our map produces the same splitting of the G-connected cover of (SFG)p as we have described in previous work, but it also induces a natural splitting of the p-completions of the component groups of fixed point subspaces.
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.1-27.
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