A suspension spectral sequence for \(v_ n\)-periodic homotopy groups (Q1898128)

We describe a category of towers of spaces in which the \(v\)-periodic homotopy groups of a space \(X\) with respect to any map \(v: \Sigma^d M\to M\) are representable. Using this description we construct a spectral sequence converging to the \(v_n\)-periodic homotopy groups of the suspension of a space \(X\) of type \(n\), with \(E^2\)-term depending only on \(v_n^{-1} \pi_* (X; M)\).