Fixed points of $p$-toral groups acting on partition complexes

Julia E. Bergner; Ruth Joachimi; Kathryn Lesh; Vesna Stojanoska; Kirsten Wickelgren

doi:10.1090/conm/641

paper

Fixed points of $p$ -toral groups acting on partition complexes

arXiv:1401.0491 · doi:10.1090/conm/641

Abstract

We consider the action of $p$ -toral subgroups of $U (n)$ on the unitary partition complex $L_{n}$ . We show that if $H \subseteq U (n)$ is $p$ -toral and has noncontractible fixed points on $L_{n}$ , then the image of $H$ in the projective unitary group $U (n) / S^{1}$ is an elementary abelian $p$ -group.

14 pages; added examples and made substantial revisions from the first version

Fixed points of p-toral groups acting on partition complexes

Abstract

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Fixed points of $p$ -toral groups acting on partition complexes