Computing trisections of 4-manifolds

  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},
  pages={10901 - 10907}
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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