Framing 3-manifolds with bare hands
Riccardo Benedetti, Paolo Lisca

TL;DR
This paper presents three elementary proofs that all closed, orientable 3-manifolds are parallelizable, avoiding advanced concepts like spin structures and Stiefel-Whitney classes.
Contribution
It introduces simplified proofs for the parallelizability of 3-manifolds that require minimal background knowledge.
Findings
All closed, orientable 3-manifolds are parallelizable.
Three proofs provided without using spin structures or Stiefel-Whitney classes.
Proofs are accessible with minimal mathematical background.
Abstract
After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.
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