The $\mathbb{Z}/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points

Abstract

We prove that the Serre spectral sequence of the fibration ${\overline{\mathcal{M}}}_{0,1+p}\to E\mathbb{Z}/p{\times }_{\mathbb{Z}/p}{\overline{\mathcal{M}}}_{0,1+p}\to B\mathbb{Z}/p$ collapses at the $E_2$ page. We use this to prove that: for any element of the $\mathbb{Z}/p$-equivariant cohomology with ${\mathbb{F}}_p$-coefficients of genus zero Deligne-Mumford space with $1+p$ marked points, if this element is torsion then it is non-equivariant. This concludes that the only "interesting" $\mathbb{Z}/p$-equivariant operations are quantum Steenrod power operations.

15 pages. This version was accepted to be published by MSP in Algebraic & Geometric Topology

References in corpus (1)

• Covariant constancy of quantum Steenrod operations