Mathematical Proceedings of the Cambridge Philosophical Society

Additivity of bridge numbers of knots

a1 Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, U.S.A. e-mail:


We provide a new proof of the following results of H. Schubert: if $K$ is a satellite knot with companion $J$ and pattern $(\skew1\hat{V}, L)$ with index $k$, then the bridge numbers satisfy the following: $b(K) \geq k \cdot (b(J))$. In addition, if $K$ is a composite knot with summands $J$ and $L$, then $b(K) = b(J) + b(L) - 1.$

(Received November 19 2001)