Additivity of bridge numbers of knots
Abstract
We provide a new proof of the following results of H. Schubert: if K is a satellite knot with companion J and pattern (skew1hat{V}, L) with index k, then the bridge numbers satisfy the following: b(K) ≥ k * (b(J)). In addition, if K is a composite knot with summands J and L, then b(K) = b(J) + b(L) - 1.
- Publication:
-
Mathematical Proceedings of the Cambridge Philosophical Society
- Pub Date:
- November 2003
- DOI:
- 10.1017/S0305004103006832
- Bibcode:
- 2003MPCPS.135..539S