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2006 Small genus knots in lens spaces have small bridge number
Kenneth L Baker
Algebr. Geom. Topol. 6(4): 1519-1621 (2006). DOI: 10.2140/agt.2006.6.1519

Abstract

In a lens space X of order r a knot K representing an element of the fundamental group π1Xr of order sr contains a connected orientable surface S properly embedded in its exterior XN(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 s4g1. Then with respect to the genus one Heegaard splitting of X, K has bridge number at most 1.

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Kenneth L Baker. "Small genus knots in lens spaces have small bridge number." Algebr. Geom. Topol. 6 (4) 1519 - 1621, 2006. https://doi.org/10.2140/agt.2006.6.1519

Information

Received: 12 June 2005; Accepted: 16 August 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1130.57004
MathSciNet: MR2253458
Digital Object Identifier: 10.2140/agt.2006.6.1519

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright © 2006 Mathematical Sciences Publishers

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