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Abstract
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We establish a correspondence between trisections of smooth, compact, oriented
-manifolds
with connected boundary and diagrams describing these trisected
-manifolds.
Such a diagram comes in the form of a compact, oriented surface with boundary together
with three tuples of simple closed curves, with possibly fewer curves than the genus of the
surface, satisfying a pairwise condition of being standard. This should be thought of as the
-dimensional
analog of a sutured Heegaard diagram for a sutured
-manifold.
We also give many foundational examples.
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Keywords
trisection, open book, Heegaard diagram, monodromy,
3-manifold, 4-manifold
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Mathematical Subject Classification 2010
Primary: 57M99
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Milestones
Received: 18 January 2017
Revised: 16 October 2017
Accepted: 30 October 2017
Published: 20 February 2018
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