The Michigan Mathematical Journal

Simultaneous Flips on Triangulated Surfaces

Valentina Disarlo and Hugo Parlier

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We investigate a type of distance between triangulations on finite-type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism, and our main results are upper bounds on the distance between triangulations that only depend on the topology of the surface.

Article information

Michigan Math. J., Volume 67, Issue 3 (2018), 451-464.

Received: 26 September 2016
Revised: 28 March 2018
First available in Project Euclid: 28 June 2018

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Zentralblatt MATH identifier

Primary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 30F60: Teichmüller theory [See also 32G15] 32G15: Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx] 57M50: Geometric structures on low-dimensional manifolds
Secondary: 05C12: Distance in graphs 05C60: Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15] 57M07: Topological methods in group theory 57M60: Group actions in low dimensions


Disarlo, Valentina; Parlier, Hugo. Simultaneous Flips on Triangulated Surfaces. Michigan Math. J. 67 (2018), no. 3, 451--464. doi:10.1307/mmj/1530151253.

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