Heegaard splittings of knot exteriors

Details Heegaard splittings of knot exteriors Heegaard splittings of knot exteriors

2006-08-05

arxiv.org/abs/math/0608137v4

Geom. Topol. Monogr. 12 (2007) 191-232

Mathematics

Geometric Topology

This is the version published by Geometry & Topology Monographs on 3 December 2007

Scientific paper

10.2140/gtm.2007.12.191

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 in S^3 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 mu-primitive.

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