Geometry & Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 12, pages 261-293.

Minimal Seifert manifolds for higher ribbon knots

James Howie

Abstract. We show that a group presented by a labelled oriented tree presentation in which the tree has diameter at most three is an HNN extension of a finitely presented group. From results of Silver, it then follows that the corresponding higher dimensional ribbon knots admit minimal Seifert manifolds.

Keywords. Ribbon knots, Seifert manifolds, LOT groups

AMS subject classification. Primary: 57Q45. Secondary: 20E06, 20F05, 57M05.

E-print: arXiv:math.GT/9810185

Submitted: 2 June 1997. Published: 23 October 1998.

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James Howie
Department of Mathematics, Heriot-Watt University
Edinburgh EH14 4AS, Scotland

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