Splittings in the Burnside ring and in SF_G

Christopher P. French

Let G be a finite p-group, p ≠ 2. We construct a map from the space J_G, defined as the fiber of ψ^k-1: B_GO → B_GSpin, to the space (SF_G)_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 (SF_G)_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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