Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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
Full-text PDF (346 kB)
References:
PDF
HTML
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
\Bibitem{FomShu21}
\by E.~A.~Fominykh, E.~V.~Shumakova
\paper Poor ideal three-edge triangulations are minimal
\jour Sibirsk. Mat. Zh.
\yr 2021
\vol 62
\issue 5
\pages 1163--1172
\mathnet{http://mi.mathnet.ru/smj7621}
\crossref{https://doi.org/10.33048/smzh.2021.62.515}
\elib{https://elibrary.ru/item.asp?id=47094267}
\transl
\jour Siberian Math. J.
\yr 2021
\vol 62
\issue 5
\pages 943--950
\crossref{https://doi.org/10.1134/S0037446621050153}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000698762500015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85115420795}
Linking options:
  • https://www.mathnet.ru/eng/smj7621
  • https://www.mathnet.ru/eng/smj/v62/i5/p1163
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024