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

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.

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

References in corpus (2)

• Equivariant topological complexity
• A new approach to the equivariant topological complexity

Cited by in corpus (1)

• Effective topological complexity of spaces with symmetries