Volume 12 (2007)

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Heegaard splittings of knot exteriors

Yoav Moriah

Geometry & Topology Monographs 12 (2007) 191–232

DOI: 10.2140/gtm.2007.12.191

arXiv: math/0608137

Abstract

The goal of this paper is to offer a comprehensive exposition of the current knowledge about Heegaard splittings of exteriors of knots in the 3-sphere. The exposition is done with a historical perspective as to how ideas developed and by whom. Several new notions are introduced and some facts about them are proved. In particular the concept of a 1/n-primitive meridian. It is then proved that if a knot K ⊂ S3 has a 1/n-primitive meridian; then nK = K# … #K n-times has a Heegaard splitting of genus nt(K) + n which has a 1-primitive meridian. That is, nK is µ-primitive.

Keywords

knot exterior, Heegaard splittings, unknotting tunnels

Mathematical Subject Classification

Primary: 57M25

Secondary: 57M05

References
Publication

Received: 4 August 2006
Revised: 30 March 2007
Accepted: 10 April 2007
Published: 3 December 2007

Authors
Yoav Moriah
Department of Mathematics
Technion
Haifa 32000
Israel