# Smoothing finite group actions on three-manifolds

## TL;DR

This paper proves that any continuous finite group action on a smooth three-manifold can be approximated arbitrarily closely by smooth actions, bridging the gap between continuous and smooth symmetries.

## Contribution

It establishes that all continuous finite group actions on three-manifolds are limits of smooth actions, providing a significant link between topological and smooth symmetries.

## Key findings

- Every continuous finite group action on a three-manifold is a uniform limit of smooth actions.
- The result applies to all finite groups acting on three-dimensional smooth manifolds.
- This advances understanding of the relationship between topological and smooth symmetries in three dimensions.

## Abstract

We show that every continuous action of a finite group on a smooth three-manifold is a uniform limit of smooth actions.