# Stratification and duality for homotopical groups.

@article{Barthel2017StratificationAD,
title={Stratification and duality for homotopical groups.},
author={Tobias Barthel and Nat{\a}lia Castellana and Drew Heard and Gabriel Valenzuela},
journal={arXiv: Algebraic Topology},
year={2017}
}`
We generalize Quillen's $F$-isomorphism theorem, Quillen's stratification theorem, the stable transfer, and the finite generation of cohomology rings from finite groups to homotopical groups. As a consequence, we show that the category of module spectra over $C^*(B\mathcal{G},\mathbb{F}_p)$ is stratified and costratified for a large class of $p$-local compact groups $\mathcal{G}$ including compact Lie groups, connected $p$-compact groups, and $p$-local finite groups, thereby giving a support… Expand
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