Rational SU(3)-equivariant cohomology theories
Algebraic Topology
2025-02-11 v1
Abstract
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 union of 18 blocks each dominated by a subgroup. For each of these blocks we identify a sheaf of rings and component structure. Taken together, this gives an abelian category A(SU(3)) designed to reflect the structure of rational SU(3)-equivariant cohomology theories, and we assemble the results from elsewhere to show that the category of rational SU(3)-spectra is Quillen equivalent to the category of differential graded objects of A(SU(3)).
Keywords
Cite
@article{arxiv.2502.06017,
title = {Rational SU(3)-equivariant cohomology theories},
author = {J. P. C. Greenlees},
journal= {arXiv preprint arXiv:2502.06017},
year = {2025}
}