On equivariant and invariant topological complexity of smooth $\mathbb{Z}/p$-spheres

Zbigniew Błaszczyk; Marek Kaluba

doi:10.1090/proc/13528

On equivariant and invariant topological complexity of smooth $\mathbb{Z}/p$-spheres

Algebraic Topology 2017-07-11 v2

Authors: Zbigniew Błaszczyk , Marek Kaluba

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

We investigate equivariant and invariant topological complexity of spheres endowed with smooth non-free actions of cyclic groups of prime order. We prove that semilinear $\mathbb{Z}/p$ -spheres have both invariants either $2$ or $3$ and calculate exact values in all but two cases for linear actions. On the other hand, we exhibit examples which show that these invariants can be arbitrarily high in the class of smooth $\mathbb{Z}/p$ -spheres.

Keywords

topological complexity equivariant topology smooth actions cyclic groups Z/p-spheres semilinear spheres linear actions

Cite

@article{arxiv.1501.07724,
  title  = {On equivariant and invariant topological complexity of smooth $\mathbb{Z}/p$-spheres},
  author = {Zbigniew Błaszczyk and Marek Kaluba},
  journal= {arXiv preprint arXiv:1501.07724},
  year   = {2017}
}

Comments

New title; minor changes to improve readability. Final version, to appear in Proc. Amer. Math. Soc. 12 pages, no figures

On equivariant and invariant topological complexity of smooth $\mathbb{Z}/p$-spheres

Abstract

Keywords

Cite

Comments

Related papers