Smoothing finite-order bilipschitz homeomorphisms of 3-manifolds

TL;DR

The paper proves that finite cyclic group actions by nearly bilipschitz homeomorphisms on closed 3-manifolds can be smoothly conjugated, bridging the gap between topological and smooth symmetries in 3D spaces.

Contribution

It establishes a quantitative smoothing result for finite cyclic group actions on 3-manifolds, showing near-bilipschitz actions are conjugate to smooth actions.

Findings

Finite cyclic group actions with (1+1/4000)-bilipschitz homeomorphisms are conjugate to smooth actions.

The result applies to all closed 3-manifolds.

Provides a quantitative threshold for smoothing group actions.

Abstract

We show that, for $\varepsilon=\dfrac{1}{4000}$, any action of a finite cyclic group by $(1+\varepsilon)$-bilipschitz homeomorphisms on a closed 3-manifold is conjugated to a smooth action.