Framing 3-manifolds with bare hands
Geometric Topology
2018-08-07 v2
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.
Cite
@article{arxiv.1806.04991,
title = {Framing 3-manifolds with bare hands},
author = {Riccardo Benedetti and Paolo Lisca},
journal= {arXiv preprint arXiv:1806.04991},
year = {2018}
}
Comments
15 pages. Expanded and more complete version. We survey a further proof available in the literature based on even surgery presentations of 3-manifolds and we provide two further "bare hands" proofs based on the existence of such presentations in a few special cases