|
|
|
Small genus knots in lens spaces have small bridge number
Kenneth L Baker
|
|
Algebraic & Geometric Topology 6
(2006) 1519–1621
|
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
|
Publication
Received: 12 June 2005
Accepted: 16 August 2006
Published: 11 October 2006
|
|
