English

Framings and Projective Framings for 3-Manifolds

Geometric Topology 2007-05-23 v1

Abstract

We give an elementary proof of the fact that any orientable 3-manifold admits a framing (i.e. is parallelizable) and any non-orientable 3-manifold admits a projective framing. The proof uses only basic facts about immersions of surfaces in 3-space.

Keywords

Cite

@article{arxiv.math/0312311,
  title  = {Framings and Projective Framings for 3-Manifolds},
  author = {Tahl Nowik},
  journal= {arXiv preprint arXiv:math/0312311},
  year   = {2007}
}
R2 v1 2026-07-22T17:00:49.933Z