Connectedness of the space of smooth actions of $\Z^n$ on the interval

TL;DR

This paper proves the connectedness of the space of smooth, orientation-preserving actions of 5^n on the interval and the space of nonfree actions of 5^2 on the circle, revealing topological properties of these action spaces.

Contribution

It establishes the connectedness of specific spaces of smooth group actions, a novel topological insight into the structure of these action spaces.

Findings

Spaces of 5^n actions on [0,1] are connected.

Nonfree 5^2 actions on the circle form a connected space.

Provides new understanding of the topology of smooth group actions.

Abstract

We prove that the spaces of $\Cinf$ orientation-preserving actions of $\Z^n$ on $[0,1]$ and nonfree actions of $\Z^2$ on the circle are connected.