Orbit Spaces of Linear Circle Actions

TL;DR

This paper demonstrates that different effective linear circle actions produce orbit spaces with distinct differential structures, highlighting the relationship between group actions and the topology of their quotient spaces.

Contribution

It establishes a link between the non-isomorphism of linear circle actions and the non-diffeomorphism of their orbit spaces, providing new insights into the structure of these spaces.

Findings

Non-isomorphic effective linear circle actions have non-diffeomorphic orbit spaces.

The differential structure of orbit spaces reflects the properties of the group actions.

The results differentiate orbit spaces based on the underlying circle actions.

Abstract

In this paper, it is shown that non-isomorphic effective linear circle actions yield non-diffeomorphic differential structures on the corresponding orbit spaces.