On detection theorems in representation theory and generalized equivariant cohomology
Event details
| Date | 19.09.2014 |
| Hour | 14:15 › 15:30 |
| Speaker | Justin Noel |
| Location | |
| Category | Conferences - Seminars |
Let G be a finite group. Artin's theorem says that we can recover the complex representation ring of G from the representations of the cyclic subgroups of G up to torsion, or additive nilpotence. Quillen's F-isomorphism theorem says that we can recover the mod-p cohomology of G from the mod-p cohomology of the elementary abelian p-subgroups of G up to multiplicative nilpotence. Both of these detection theorems can be restated as results in equivariant stable homotopy theory.
We construct and apply a general framework for proving analogues of these theorems in this context. As special cases we recover the above theorems as well as analogues for integral cohomology (due to Carlson), KO (partially due to Fausk), ko, complex oriented theories (partially due to Hopkins-Kuhn-Ravenel), the many variants of topological modular forms, Ln-local spectra, and classical cobordism theories.
This is joint work with Akhil Mathew and Niko Naumann.
We construct and apply a general framework for proving analogues of these theorems in this context. As special cases we recover the above theorems as well as analogues for integral cohomology (due to Carlson), KO (partially due to Fausk), ko, complex oriented theories (partially due to Hopkins-Kuhn-Ravenel), the many variants of topological modular forms, Ln-local spectra, and classical cobordism theories.
This is joint work with Akhil Mathew and Niko Naumann.
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- Free
Organizer
- Kathryn Hess