Every knot has characterising slopes

Author: 

Lackenby, M

Publication Date: 

8 October 2018

Journal: 

Mathematische Annalen

Last Updated: 

2019-07-10T05:46:24.34+01:00

abstract: 

Let K be a knot in the 3-sphere. A slope p/q is said to be characterising for
K if whenever p/q surgery on K is homeomorphic, via an orientation-preserving
homeomorphism, to p/q surgery on another knot K' in the 3-sphere, then K and K'
are isotopic. It was an old conjecture of Gordon, proved by Kronheimer, Mrowka,
Ozsvath and Szabo, that every slope is characterising for the unknot. In this
paper, we show that every knot K has infinitely many characterising slopes,
confirming a conjecture of Baker and Motegi. In fact, p/q is characterising for
K provided |p| is at most |q| and |q| is sufficiently large.

Symplectic id: 

708228

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article