AN ESTIMATE OF HEMPEL DISTANCE FOR BRIDGE SPHERES

Title & Authors
AN ESTIMATE OF HEMPEL DISTANCE FOR BRIDGE SPHERES
Ido, Ayako;

Abstract
Tomova [8] gave an upper bound for the distance of a bridge surface for a knot with two different bridge positions in a 3-manifold. In this paper, we show that the result of Tomova [8, Theorem 10.3] can be improved in the case when there are two different bridge spheres for a link in $\small{S^3}$.
Keywords
Heegaard splitting;bridge decomposition;distance;
Language
English
Cited by
1.
Bridge splittings of links with distance exactly n, Topology and its Applications, 2015, 196, 608
References
1.
D. Bachman and S. Schleimer, Distance and bridge position, Pacific J. Math. 219 (2005), no. 2, 221-235.

2.
K. Hartshorn, Heegaard splittings of Haken manifolds have bounded distance, Pacific J. Math. 204 (2002), no. 1, 61-75.

3.
C. Hayashi and K. Shimokawa, Thin position of a pair (3-manifold, 1-submanifold), Pacific J. Math. 197 (2001), no. 2, 301-324.

4.
J. Hempel, 3-manifolds as viewed from the curve complex, Topology 40 (2001), no. 3, 631-657.

5.
Y. Jang, Distance of bridge surfaces for links with essential meridional spheres, Pacific J. Math. 267 (2014), no. 1, 121-130.

6.
J. Johnson and M. Tomova, Flipping bridge surfaces and bounds on the stable bridge number, Algebr. Geom. Topol. 11 (2011), no. 4, 1987-2005.

7.
M. Scharlemann andn M. Tomova, Alternate Heegaard genus bounds distance, Geom. Topol. 10 (2006), 593-617.

8.
M. Tomova, Multiple bridge surfaces restrict knot distance, Algebr. Geom. Topol. 7 (2007), 957-1006.