G-index, topological dynamics and marker property

2020/12/30 by Tsukamoto, Masaki, Tsutaya, Mitsunobu, Yoshinaga, Masahiko · 3 citations
#37B05 #55M35 #Algebraic Topology (math.AT) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.15372

Abstract

Given an action of a finite group G, we can define its index. The G-index roughly measures a size of the given G-space. We explore connections between the G-index theory and topological dynamics. For a fixed-point free dynamical system, we study the ℤ_p-index of the set of p-periodic points. We find that its growth is at most linear in p. As an application, we construct a free dynamical system which does not have the marker property. This solves a problem which has been open for several years.

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