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High Distance Bridge Surfaces
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.Comment: 17 pages, 13 figures; v2 clarifying revisions made based on referee's
comment
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