Only finitely many alternating knots can yield a given manifold by surgery

Abstract

We show that given a 3-manifold $Y$ there is only a finite number of alternating knots $K\subset S^3$ such that $Y$ can be obtained by surgery on $K$. A very similar but somewhat not complete statement has been obtained in a recent preprint of Lackenby and Purcell.

This paper has been withdrawn because it was merged into a single paper with another paper by the author (arXiv:1411.1275)

References in corpus (1)

• Floer homology and knot complements