High Distance Bridge Surfaces

Ryan Blair; Maggy Tomova; Michael Yoshizawa

doi:10.2140/agt.2013.13.2925

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arXiv · 1203.4294

High Distance Bridge Surfaces

Ryan Blair·Maggy Tomova·Michael Yoshizawa

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Abstract

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 Sigma 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 \cup S' such that M contains a c-component tangle T with a bridge surface Sigma of genus g that separates the boundary of M into S and S', |T \cap Sigma|=2b and T intersects S and S' exactly in their marked points, and Sigma has distance at least n.

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Ryan Blair, Maggy Tomova, Michael Yoshizawa. 2013-07-26. High Distance Bridge Surfaces. https://doi.org/10.2140/agt.2013.13.2925

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