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Sibirskii Matematicheskii Zhurnal, 2021, Volume 62, Number 5, Pages 1163–1172
DOI: https://doi.org/10.33048/smzh.2021.62.515 (Mi smj7621) 		 
Poor ideal three-edge triangulations are minimal

E. A. Fominykhab, E. V. Shumakovaac

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences, St. Petersburg, Russia
c Chelyabinsk State University, Chelyabinsk, Russia
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DOI: https://doi.org/10.33048/smzh.2021.62.515
Abstract: An ideal triangulation of a compact 3-manifold with nonempty boundary is known to be minimal if and only if the triangulation contains the minimum number of edges among all ideal triangulations of the manifold. Therefore, every ideal one-edge triangulation (i.e., an ideal singular triangulation with exactly one edge) is minimal. Vesnin, Turaev, and Fominykh showed that an ideal two-edge triangulation is minimal if no 3–2 Pachner move can be applied. In this paper we show that each of the so-called poor ideal three-edge triangulations is minimal. We exploit this property to construct minimal ideal triangulations for an infinite family of hyperbolic 3-manifolds with totally geodesic boundary.
Keywords: 3-manifold, ideal triangulation, triangulation complexity of the 3-manifold, minimal triangulation.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00741
The authors were supported by the Russian Foundation for Basic Research (Grant 19–01–00741).
Received: 16.03.2021
Revised: 12.05.2021
Accepted: 11.06.2021
English version:
Siberian Mathematical Journal, 2021, Volume 62, Issue 5, Pages 943–950
DOI: https://doi.org/10.1134/S0037446621050153
Bibliographic databases:
Document Type: Article
UDC: 515.162
MSC: 35R30
Language: Russian
Citation: E. A. Fominykh, E. V. Shumakova, “Poor ideal three-edge triangulations are minimal”, Sibirsk. Mat. Zh., 62:5 (2021), 1163–1172; Siberian Math. J., 62:5 (2021), 943–950
Citation in format AMSBIB
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