Elementary abelian 2-groups actions and complexes of unstable modulues

Time: 15:00 to  17:00 Ngày 01/06/2017

Venue/Location: C2-714

Content:

Let $X$ be a finite comple with an action of an elementary abelian $2$-group $V_n$. One associates to this situation a complex, co-augmented by the equivariant cohomology, of $\F2[x_1,\ldots, x_n] \cong H^*V_n$ modules (where the action is compatible with the one one of the Steenrod algebra). This complex is acyclic if and only if the equivariant cohomology is free as as $H^*V_n$-module. One then discuss particular cases related to the Steinberg representation and make a conjecture about Brown-Gitler spectra.