International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 583-589

The Heegaard genus of manifolds obtained by surgery on links and knots

Bradd Clark

Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USA

Received 15 January 1979

Copyright © 1980 Bradd Clark. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let LS3 be a fixed link. It is shown that there exists an upper bound on the Heegaard genus of any manifold obtained by surgery on L. The tunnel number of L, T(L), is defined and used as an upper bound. If K is a double of the knot K, it is shown that T(K)T(K)+1. If M is a manifold obtained by surgery on a cable link about K which has n components, it is shown that the Heegaard genus of M is at most T(K)+n+1.