Spectra of subrings of cohomology generated by characteristic classes for fusion systems
Abstract
If $\mathcal{F}$ is a saturated fusion system on a finite $p$group $S$, we define the Chern subring $Ch(\mathcal{F})$ of $\mathcal{F}$ to be the subring of the mod$p$ cohomology $H^*(S)$ of $S$ generated by the Chern classes of $\mathcal{F}$stable representations of $S$. We show that $Ch(\mathcal{F})$ is contained in $H^*(\mathcal{F})$ and apply a result of Green and the first author to describe its spectrum in terms of a certain category of elementary abelian subgroups of $S$. We obtain similar results for various related subrings, including those generated by characteristic classes of $\mathcal{F}$stable $S$sets.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.10701
 arXiv:
 arXiv:2404.10701
 Bibcode:
 2024arXiv240410701L
 Keywords:

 Mathematics  Group Theory;
 20J06;
 20D20
 EPrint:
 14 pages