# Null-homologous framing?

1. Jan 21, 2014

### WWGD

Hi, all:

I'm trying to understand the meaning of the term "null-homotopic framing".

Say K is a knot embedded in a manifold , and N(K) is a tubular neighborhood of K

( there is a theorem that a compact submanifold allows for the existence of a tubular

neighborhood).

I read about it here, under " motivation for the Legendrian conjecture " :

http://electrichandleslide.wordpress.com/2013/05/17/the-legendrian-surgery-conjecture/

A framing here is a choice ( up to isotopy, I believe; not specified in Rolfsen's book) of

isomorphism between the tubular neighborhood N(K) and $S^1 \times D^2$.

(Though K can be any manifold for which a tubular neighborhood exists, e.g., maybe

the normal bundle N(K) is trivial, or K is compact, embedded in some ambient manifold M)

I understand the obvious meaning of null-homologous for a cycle in any space, meaning

that the cycle is , e.g., a bounding cycle (cycle with non-trivial boundary) in simplicial homology,

so homologically trivial, or different definitions for different choices of homology, but I cannot see what a

null-homologous framing is. Any ideas?

Thanks.

Last edited: Jan 22, 2014