# Computing trisections of 4-manifolds

@article{Bell2018ComputingTO,
title={Computing trisections of 4-manifolds},
author={Mark C. Bell and Joel Hass and Joachim Hyam Rubinstein and Stephan Tillmann},
journal={Proceedings of the National Academy of Sciences},
year={2018},
volume={115},
pages={10901 - 10907}
}
• Published 7 November 2017
• Mathematics
• Proceedings of the National Academy of Sciences
Significance Algorithms that decompose a manifold into simple pieces reveal the geometric and topological structure of the manifold, showing how complicated structures are constructed from simple building blocks. This note describes a way to algorithmically construct a trisection, which describes a four-dimensional manifold as a union of three four-dimensional 1-handlebodies. The complexity of the 4-manifold is captured in a collection of curves on a surface, which guide the gluing of the 1…

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