3-primary v1-periodic homotopy groups of E7

Abstract

We compute the 3-primary v1-periodic homotopy groups of the exceptional Lie group E7. Now E8 at the primes 3 and 5 is the only compact simple Lie group whose odd-primary v1-periodic homotopy groups remian to be computed. The main work is computing the unstable Novikov spectral sequence of ΩE7/Sp(2). Showing that this converges to v1-periodic homotopy groups requires recent work of Bousfield and Bendersky-Thompson.