%0 Journal Article
%T Only finitely many alternating knots can yield a given manifold by surgery
%A Fyodor Gainullin
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1411.2249v2