Spaces of subgroups of toral groups
Algebraic Topology
2025-10-20 v2 Group Theory
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.
Cite
@article{arxiv.2501.06914,
title = {Spaces of subgroups of toral groups},
author = {J. P. C. Greenlees},
journal= {arXiv preprint arXiv:2501.06914},
year = {2025}
}
Comments
Version 2: Corrected typos and improved discussion of Weyl group method