Diagrams for Relative Trisections

Nickolas A. Castro; David T. Gay; Juanita Pinzón-Caicedo

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arXiv · 1610.06373

Diagrams for Relative Trisections

Nickolas A. Castro·David T. Gay·Juanita Pinzón-Caicedo

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Abstract

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.

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BibTeX RIS

Nickolas A. Castro, David T. Gay, Juanita Pinzón-Caicedo. 2016-10-20. Diagrams for Relative Trisections. https://arxiv.org/abs/1610.06373

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