On the iterated complex transfer (Q1117498)

This work is a sequel to the work of \textit{D. Carlisle}, \textit{P. Eccles}, \textit{S. Hilditch}, \textit{N. Ray}, \textit{L. Schwartz}, \textit{G. Walker}, and \textit{R. Wood} [Math. Z. 189, 239-261 (1985; Zbl 0536.55006)]. The basic object of study is the iterated transfer map \[ t(n): \Sigma^ n(CP^{\infty}_+)\wedge...\wedge (CP^{\infty}_+)\quad \to \quad S^ 0, \] where there are n copies of \(CP^{\infty}_+\) smashed together. This map is used to connect the results of the above-mentioned paper with other studies of \(\Sigma CP^{\infty}\times...\times CP^{\infty}\). Then the authors improve a result in the cited paper, using Morava K-theory, showing that certain members of the \(\beta\)-family can be represented by framed hypersurfaces.