Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

@inproceedings{Verdire2014DiscreteSI,
  title={Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces},
  author={{\'E}ric Colin de Verdi{\`e}re and Alfredo Hubard and Arnaud de Mesmay},
  booktitle={Symposium on Computational Geometry},
  year={2014}
}
How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given combinatorial map in triangulated combinatorial surfaces (or their dual cross-metric counterpart). Our work builds upon Riemannian systolic inequalities, which bound the minimum length of non-trivial closed curves in terms of the genus and the area of the… CONTINUE READING
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