Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

  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},
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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Algebraic topology

  • Allen Hatcher
  • 2002
Highly Influential
5 Excerpts

Geometry and spectra of compact Riemann surfaces, volume 106 of Progress

  • Peter Buser
  • Mathematics. Birkhäuser,
  • 1992
Highly Influential
11 Excerpts

Filling Riemannian manifolds

  • Mikhael Gromov
  • Journal of Differential Geometry,
  • 1983
Highly Influential
10 Excerpts

Sabourau. Entropy of systolically extremal surfaces and asymptotic 548

  • Mikhail G. Katz, Stéphane
  • bounds. arXiv:math/041031,
  • 2004
Highly Influential
6 Excerpts

On the genus of a random riemann surface. In Complex 528 Manifolds and Hyperbolic Geometry, number 311 in Contemporary Mathematics, pages 133–140

  • Alexander Gamburd, Eran Makover
  • AMS,
  • 2002
Highly Influential
6 Excerpts

Pants decompositions of random surfaces

  • Larry Guth, Hugo Parlier, Robert Young
  • Geometric 540 and Functional Analysis,
  • 2011
Highly Influential
3 Excerpts

Classical topology and combinatorial group theory

  • John Stillwell
  • 1980
Highly Influential
3 Excerpts

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