Algebraic & Geometric Topology 6 (2006) 1519–1621

DOI: 10.2140/agt.2006.6.1519

arXiv: math.GT/0612427

Abstract

In a lens space X of order r a knot K representing an element of the fundamental group π₁ X ≈ Z/rZ of order s ≤ r contains a connected orientable surface S properly embedded in its exterior X-N(K) such that ∂ 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.

Keywords

(1,1)–knots, Berge knots, bridge position, lens space, Scharlemann cycle, thin position

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M25

References

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Publication

Received: 12 June 2005
Accepted: 16 August 2006
Published: 11 October 2006

Authors