The \(v_ 1\)-periodic unstable Novikov spectral sequence
Let \(p\) be a prime. The \(p\)-primary \(v_ 1\)-periodic homotopy groups \(v_ 1^{-1}\pi_ *(X)\) of a space \(X\) are defined as a direct limit. These groups contain obstructions to a number of important geometrical problems; e.g. James numbers. In this paper the author defines the \(v_ 1\)-local Unstable Novikov Spectral Sequence and, in the case of compact, \(p\)-torsion free Lie groups, shows how the localized spectral sequence determines the periodic homotopy at odd primes. Since the periodic Unstable Novikov Spectral Sequence converges for the odd spheres, the problem of calculating the periodic homotopy groups reduces to an algebraic problem.
scientific article; zbMATH DE number 54631
scientific article