Subject: Re: two questions
Date: Mon, 11 Mar 2002 15:36:37 -0500 (EST)
From: Dev Sinha
> when the frenet frame of a smoosh closed space curve traces
> the curve one turn,endpoint of its normal vector constructs another
> curve in space. these two curves have a linking number.
> What this linking number means, is there anything about it in
> litrature?
This number is often called the self-linking number. It is often
attributed to Pohl:
36 #5827 Pohl, William F. The self-linking number of a closed space curve.
J. Math. Mech. 17 1967/1968
975--985. (Reviewer: L. Neuwirth) 53.01
Searching Mathscinet with keyword "self-linking" thirteen references come
up, including a much older article of Blanchfield and Fox. For polygonal
curves, a version was defined by Banchoff.
Recently, Bott and Taubes and others have included this self-linking
number as one of (in fact, the simplest of) the finite-type
knot invariants.
-Dev