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1998 A natural framing of knots
Michael T Greene, Bert Wiest
Geom. Topol. 2(1): 31-64 (1998). DOI: 10.2140/gt.1998.2.31


Given a knot K in the 3–sphere, consider a singular disk bounded by K and the intersections of K with the interior of the disk. The absolute number of intersections, minimised over all choices of singular disk with a given algebraic number of intersections, defines the framing function of the knot. We show that the framing function is symmetric except at a finite number of points. The symmetry axis is a new knot invariant, called the natural framing of the knot. We calculate the natural framing of torus knots and some other knots, and discuss some of its properties and its relations to the signature and other well-known knot invariants.


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Michael T Greene. Bert Wiest. "A natural framing of knots." Geom. Topol. 2 (1) 31 - 64, 1998.


Received: 4 August 1997; Accepted: 19 March 1998; Published: 1998
First available in Project Euclid: 21 December 2017

zbMATH: 0891.57010
MathSciNet: MR1608684
Digital Object Identifier: 10.2140/gt.1998.2.31

Primary: 57M25
Secondary: 20F05

Keywords: Cayley graph , framing , knot , knot invariant , link , natural framing , torus knot

Rights: Copyright © 1998 Mathematical Sciences Publishers


Vol.2 • No. 1 • 1998
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