Diagrams for Relative Trisections

By N. Castro, David T. Gay, Juanita Pinz'on-Caicedo. 2016

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/47a4f5132805fc55053844fcbadc8dea6a6ac917