Homotopy inverse limits of Thom spectra
When \(K\) is a compact Lie group and \(V\) a real representation of \(K\), and \(n\) a positive integer, \(BK^{-nV}\) is the Thom spectrum of the virtual representation \(-nV\). The purpose of this paper is to analyze the \(p\)-adic completion of the homotopy inverse limit of \[ BK^{-1} \leftarrow BK^{-2V} \leftarrow \dots \leftarrow BK^{-nV} \leftarrow \dots \] The answer is expressed in terms of a finite tower of spectra whose fibres are specifically identified. Using the work of \textit{L. G. Lewis jun., J. P. May} and \textit{M. Steinberger} [Equivariant stable homotopy theory, Lect. Notes Math. 1213 (1986; Zbl 0611.55001)], the Thom spectra are expressed as the \(K\)-fixed point spectra of function spectra. The techniques include [\textit{M. Feshbach}, Topology 26, 1-20 (1987; Zbl 0606.57024), \textit{J. Caruso, J. P. May} and \textit{S. B. Priddy}, ibid., 413-433 (1987; Zbl 0699.55010)].
scientific article; zbMATH DE number 722025