Vol. 294, No. 2, 2018

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Diagrams for relative trisections

Nickolas A. Castro, David T. Gay and Juanita Pinzón-Caicedo

Vol. 294 (2018), No. 2, 275–305

We establish a correspondence between trisections of smooth, compact, oriented 4-manifolds with connected boundary and diagrams describing these trisected 4-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 4-dimensional analog of a sutured Heegaard diagram for a sutured 3-manifold. We also give many foundational examples.

trisection, open book, Heegaard diagram, monodromy, 3-manifold, 4-manifold
Mathematical Subject Classification 2010
Primary: 57M99
Received: 18 January 2017
Revised: 16 October 2017
Accepted: 30 October 2017
Published: 20 February 2018
Nickolas A. Castro
Department of Mathematics
University of California, Davis
One Shields Ave
Davis, CA 95616
United States
David T. Gay
Euclid Lab
160 Milledge Terrace
Athens, GA 30606
United States
Juanita Pinzón-Caicedo
Department of Mathematics
NC State University
2108 SAS Hall
Raleigh, NC 27695
United States