collaborators

8 papers

math.AT2026

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

J. P. C. Greenlees

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 fini…

math.AT2025

Spaces of subgroups of toral groups

J. P. C. Greenlees

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 sheave…

math.GR2025

The spectral space of conjugacy classes of subgroups of a compact Lie group

J. P. C. Greenlees

The space of conjugacy classes of subgroups of a compact Lie groups with its Zariski topology splits as a disjoint union of clopen blocks, each dominated by a subgroup H with finit…

math.AT2025

Rational G-spectra over blocks with finite Weyl groups

J. P. C. Greenlees

We show that for any clopen collection X of subgroups of G with finite Weyl groups, the category of G-spectra with geometric isotropy in X is equivalent to the category of equivari…

math.AT2025

Rational SU(3)-equivariant cohomology theories

J. P. C. Greenlees

We describe the spectral space of conjugacy classes of subgroups of SU(3), together with the additional structure of a sheaf of rings and a component structure. It is a disjoint un…

math.AT2025

An algebraic model for rational U(2)-spectra

J. P. C. Greenlees

We construct an explicit and calculable models for rational U(2)-spectra. This is obtained by assembling seven blocks obtained in previous work: the toral part and earlier work on…