Spaces of subgroups of toral groups

2025/01/12 by Greenlees, J. P. C. · 2 citations
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2501.06914

Abstract

We study the space of conjugacy classes of subgroups of a compact Lie group G whose identity component is a torus, and consider how various invariants of subgroups behave as sheaves over this space. This feeds in to the author's programme to give algebraic models of rational G-equivariant cohomology theories. The methods are illustrated by making the outcome explicit for all toral subgroups of compact connected rank 2 groups.

Cited by

• The spectral space of conjugacy classes of subgroups of a compact Lie group
• Rational G-spectra over blocks with finite Weyl groups

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