The quasi \(KO\)-types of weighted mod 4 lens spaces
Two spectra \(X\) and \(Y\) are said to have the same quasi \(KO_*\)-type if there is an equivalence \(KO\wedge X\to KO\wedge Y\) of \(KO\)-module spectra. The weighted mod 4 lens space \(L(s,n-s)\) is the quotient by \({\mathbf Z}/4\) of \(S^{2n+1}\) with the \(S^1\)-action defined by \[ \lambda\cdot(x_0,\ldots,x_n)=(\lambda^2x_0,\ldots, \lambda^2x_{s-1},x_s,\ldots,x_n). \] The quasi \(KO_*\)-types of the spaces \(L(s,n-s)\) are classified, depending on mod 4 values of \(s\) and \(n\), as wedges of one or two explicit complexes with no more than 6 cells.
scientific article; zbMATH DE number 1270295