8 papers
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…
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…
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…
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…
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…
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…