Divergent coindex sequence for dynamical systems

Abstract

When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a fixed-point free dynamical system, the set of p-periodic points admits a natural free action of Z/pZ for each prime number p. We are interested in the growth of its index and coindex as p → ∞. Our main result shows that there exists a fixed-point free dynamical system having the divergent coindex sequence. This solves a problem posed by [TTY20].