Every knot has characterising slopes

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 Kronhe...

وصف كامل

التفاصيل البيبلوغرافية
المؤلف الرئيسي: Lackenby, M
التنسيق: Journal article
منشور في: Springer Berlin Heidelberg 2018
الوصف
الملخص: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, Ozsváth and Szabó, 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.