𝑣₁-periodic homotopy groups of exceptional Lie groups: torsion-free cases

Abstract

The v 1 {v_1} -periodic homotopy groups v 1 − 1 π ∗ ( X ; p ) v_1^{ - 1}{\pi _ {\ast } }(X;p) are computed explicitly for all pairs ( X , p ) (X,p) , where X X is an exceptional Lie group whose integral homology has no p p -torsion. This yields new lower bounds for p p -exponents of actual homotopy groups of these spaces. Delicate calculations with the unstable Novikov spectral sequence are required in the proof.