Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point
Abstract
We are dealing with the question whether every group or semigroup action (with some additional property) on a continuum (with some additional property) has a fixed point. One of such results was given in 2009 by Shi and Sun. They proved that every nilpotent group action on a uniquely arcwise connected continuum has a fixed point. We are seeking for this type of results with e.g. commutative, compact or torsion groups and semigroups acting on dendrites, dendroids, -dendroids and uniquely arcwise connected continua. We prove that every continuous action of a compact or torsion group on a uniquely arcwise connected continuum has a fixed point. We also prove that every continuous action of a compact and commutative semigroup on a uniquely arcwise connected continuum or on a tree-like continuum has a fixed point.
Cite
@article{arxiv.1709.00852,
title = {Every continuous action of a compact group on a uniquely arcwise connected continuum has a fixed point},
author = {Benjamin Vejnar},
journal= {arXiv preprint arXiv:1709.00852},
year = {2017}
}