Geodesic
High distance bridge surfaces
Blair, Ryan1 ; Tomova, Maggy2 ; Yoshizawa, Michael3
1Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33 Street, Philadelphia, PA 19104-6395, USA
2Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA
3Department of Mathematics, University of California, Santa Barbara, South Hall, Room 6607, Santa Barbara, CA 93106-3080, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 2925-2946
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Given integers b, c, g and n, we construct a manifold M containing a c–component link L so that there is a bridge surface Σ for (M,L) of genus g that intersects L in 2b points and has distance at least n. More generally, given two possibly disconnected surfaces S and S′, each with some even number (possibly zero) of marked points, and integers b, c, g and n, we construct a compact, orientable manifold M with boundary S ∪ S′ such that M contains a c–component tangle T with a bridge surface Σ of genus g that separates ∂M into S and S′, |T ∩ Σ| = 2b and T intersects S and S′ exactly in their marked points, and Σ has distance at least n.

DOI : 10.2140/agt.2013.13.2925
Classification : 57M25, 57M50
Keywords: bridge surfaces, bridge distance

Blair, Ryan  1   ; Tomova, Maggy  2   ; Yoshizawa, Michael  3

1 Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 South 33 Street, Philadelphia, PA 19104-6395, USA
2 Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242-1419, USA
3 Department of Mathematics, University of California, Santa Barbara, South Hall, Room 6607, Santa Barbara, CA 93106-3080, USA 
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Blair, Ryan; Tomova, Maggy; Yoshizawa, Michael. High distance bridge surfaces. Algebraic and Geometric Topology, Tome 13 (2013) no. 5, pp. 2925-2946. doi: 10.2140/agt.2013.13.2925

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[4] J Johnson, M Tomova, Flipping bridge surfaces and bounds on the stable bridge number, Algebr. Geom. Topol. 11 (2011) 1987

[5] M Tomova, Multiple bridge surfaces restrict knot distance, Algebr. Geom. Topol. 7 (2007) 957

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