Non-leaving-face property for marked surfaces

Thomas Brüstle; Jie Zhang

doi:10.1007/s11464-019-0767-7

Non-leaving-face property for marked surfaces

Thomas Brüstle, Jie Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Université de Sherbrooke

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider the polytope arising from a marked surface by flips of triangulations. D. D. Sleator, R. E. Tarjan, and W. P. Thurston [J. Amer. Math. Soc., 1988, 1(3): 647–681] studied the diameter of the associahedron, which is the polytope arising from a marked disc by flips of triangulations. They showed that every shortest path between two vertices in a face does not leave that face. We give a new method, which is different from the one used by V. Disarlo and H. Parlier [arXiv: 1411.4285] to establish the same non-leaving-face property for all unpunctured marked surfaces.

Original language	English
Pages (from-to)	521-534
Number of pages	14
Journal	Frontiers of Mathematics in China
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s11464-019-0767-7
Publication status	Published - 1 Jun 2019

Keywords

Marked surface
exchange graph
non-leaving-face property

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10.1007/s11464-019-0767-7

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AB - We consider the polytope arising from a marked surface by flips of triangulations. D. D. Sleator, R. E. Tarjan, and W. P. Thurston [J. Amer. Math. Soc., 1988, 1(3): 647–681] studied the diameter of the associahedron, which is the polytope arising from a marked disc by flips of triangulations. They showed that every shortest path between two vertices in a face does not leave that face. We give a new method, which is different from the one used by V. Disarlo and H. Parlier [arXiv: 1411.4285] to establish the same non-leaving-face property for all unpunctured marked surfaces.

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Non-leaving-face property for marked surfaces

Abstract

Keywords

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