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

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

Algebraic Topology 2015-12-09 v3

Authors: Julia E. Bergner , Ruth Joachimi , Kathryn Lesh , Vesna Stojanoska , Kirsten Wickelgren

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Abstract

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

Keywords

p-toral groups partition complexes fixed points unitary group projective unitary group elementary abelian p-group homotopy theory

Cite

@article{arxiv.1401.0491,
  title  = {Fixed points of $p$-toral groups acting on partition complexes},
  author = {Julia E. Bergner and Ruth Joachimi and Kathryn Lesh and Vesna Stojanoska and Kirsten Wickelgren},
  journal= {arXiv preprint arXiv:1401.0491},
  year   = {2015}
}

Comments

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

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

Abstract

Keywords

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