Vol. 40, No. 3, 1972

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Two bridge knots are alternating knots

Richard Goodrick

Vol. 40 (1972), No. 3, 561–564

H. Schubert introduced a numerical knot invariant called the bridge number of a knot. In particular, he classified the two-bridge knots and proved that they were prime knots. Later, Murasugi showed that if K is an alternating knot then the matrix of K is alternating. The latter is true of twobridge knots. The purpose of the following is to give a somewhat unusual geometric presentation of two-bridge knots from which it will be seen that they are alternating knots.

Mathematical Subject Classification
Primary: 55A25
Received: 24 August 1970
Published: 1 March 1972
Richard Goodrick