Corpus ID: 220525431

Cubic graphs induced by bridge trisections

@article{Meier2020CubicGI,
  title={Cubic graphs induced by bridge trisections},
  author={J. Meier and A. Thompson and A. Zupan},
  journal={arXiv: Geometric Topology},
  year={2020}
}
Every embedded surface $\mathcal{K}$ in the 4-sphere admits a bridge trisection, a decomposition of $(S^4,\mathcal{K})$ into three simple pieces. In this case, the surface $\mathcal{K}$ is determined by an embedded 1-complex, called the $\textit{1-skeleton}$ of the bridge trisection. As an abstract graph, the 1-skeleton is a cubic graph $\Gamma$ that inherits a natural Tait coloring, a 3-coloring of the edge set of $\Gamma$ such that each vertex is incident to edges of all three colors. In this… Expand

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