paper

Framings and Projective Framings for 3-Manifolds

arXiv:math/0312311

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.

Framings and Projective Framings for 3-Manifolds · wovepaper