# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1704.04519