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High distance bridge surfaces

Ryan Blair, Maggy Tomova and Michael Yoshizawa

Algebraic & Geometric Topology 13 (2013) 2925–2946

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.

bridge surfaces, bridge distance
Mathematical Subject Classification 2010
Primary: 57M25, 57M50
Received: 19 April 2012
Revised: 11 April 2013
Accepted: 23 April 2013
Published: 26 July 2013
Ryan Blair
Department of Mathematics
University of Pennsylvania
David Rittenhouse Lab
209 South 33 Street
Philadelphia, PA 19104-6395
Maggy Tomova
Department of Mathematics
University of Iowa
14 MacLean Hall
Iowa City, IA 52242-1419
Michael Yoshizawa
Department of Mathematics
University of California, Santa Barbara
South Hall, Room 6607
Santa Barbara, CA 93106-3080