Algebraic models of rational equivariant cohomology theories
Event details
| Date | 24.05.2016 |
| Hour | 10:15 › 11:30 |
| Speaker |
John Greenlees (University of Sheffield) |
| Location |
CM113
|
| Category | Conferences - Seminars |
(joint work with D.Barnes, M.Kedziorek and B.Shipley).
For a compact Lie group G, G-equivariant cohomology theories are represented by G-spectra, so the category of cohomology theories and natural transformations is the homotopy category of the model category of G-spectra. It is now known for a variety of groups that the category of rational-G-spectra is Quillen equivalent to differential graded objects in an abelian category A(G).
The talk will summarise the status of the conjecture that this is true for all groups G, but the emphasis will be on the description of the category A(G) for various different groups G and in various styles. Since a guiding principle says the category of rational-G-spectra is the category of equivariant modules over the sphere spectrum S, we can view this as describing a geometric object Proj(S^G).
For a compact Lie group G, G-equivariant cohomology theories are represented by G-spectra, so the category of cohomology theories and natural transformations is the homotopy category of the model category of G-spectra. It is now known for a variety of groups that the category of rational-G-spectra is Quillen equivalent to differential graded objects in an abelian category A(G).
The talk will summarise the status of the conjecture that this is true for all groups G, but the emphasis will be on the description of the category A(G) for various different groups G and in various styles. Since a guiding principle says the category of rational-G-spectra is the category of equivariant modules over the sphere spectrum S, we can view this as describing a geometric object Proj(S^G).
Links
Practical information
- Informed public
- Free
Organizer
- Magdalena Kedziorek