The rational homotopy groups of virtual spheres for rank 1 compact Lie groups

Abstract

We calculate the rational representation-ring-graded stable stems for rank 1 groups, SU(2), SO(3), Pin (2), O(2), Spin(2) and SO(2), in the same spirit as the calculations for finite groups in arXiv:2205.02382 with J.D.Quigley. This illustrates the effectiveness of the algebraic models for these categories of G-spectra, and the way tom Dieck splitting fails for desuspensions. [v4: typos and tweaks in wording]

Version 3: Corrected more typos, expanded explanations. Corrected summary of model in semisimple cases