A free action of a finite group on 3-sphere equivalent to a linear action

TL;DR

This paper proves that any free action of a finite group on a 3-sphere is equivalent to a linear action, using cobordism and Morse theory techniques, confirming the Space-Form-Conjecture.

Contribution

It provides a proof of the Space-Form-Conjecture, establishing the equivalence of free finite group actions on 3-spheres to linear actions.

Findings

Confirmed the Space-Form-Conjecture for 3-spheres

Demonstrated the use of cobordism and Morse theory in group action classification

Established that all free finite group actions on 3-spheres are linear

Abstract

In this paper, by use of techniques associated to Cobordism theory and Morse theory, we give a proof of Space-Form-Conjecture, i.e. a free action of a finite group on 3-manifold is equivalent to a linear action.