Small genus knots in lens spaces have small bridge number

Details Small genus knots in lens spaces have small bridge number Small genus knots in lens spaces have small bridge number

2006-12-15

arxiv.org/abs/math/0612427v2

Algebr. Geom. Topol. 6 (2006) 1519-1621

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 11 October 2006

Scientific paper

10.2140/agt.2006.6.1519

In a lens space X of order r a knot K representing an element of the fundamental group pi_1 X = Z/rZ of order s <= r contains a connected orientable surface S properly embedded in its exterior X-N(K) such that the boundary of S intersects the meridian of K minimally s times. Assume S has just one boundary component. Let g be the minimal genus of such surfaces for K, and assume s >= 4g-1. Then with respect to the genus one Heegaard splitting of X, K has bridge number at most 1.

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