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

J. P. C. Greenlees

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arXiv · 2506.18085

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

J. P. C. Greenlees

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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]

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BibTeX RIS

J. P. C. Greenlees. 2025-06-22. The rational homotopy groups of virtual spheres for rank 1 compact Lie groups. https://arxiv.org/abs/2506.18085

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