2016/10/20 by Castro, Nickolas A., Gay, David T., Pinzón-Caicedo, Juanita · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1610.06373
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 standardness condition. 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.