On Stiefel's parallelizability of 3-manifolds

TL;DR

This paper presents a new elementary proof demonstrating that all closed orientable 3-manifolds are parallelizable, utilizing Heegaard splittings as the main tool.

Contribution

It provides a novel, elementary proof of Stiefel's parallelizability theorem for 3-manifolds based on Heegaard splittings.

Findings

All closed orientable 3-manifolds are parallelizable.

Heegaard splittings are effective in proving parallelizability.

The proof simplifies previous approaches to this topological property.

Abstract

We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.