RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2015, Volume 288, Pages 38–48 (Mi tm3608)  

This article is cited in 2 scientific papers (total in 2 papers)

Three-dimensional manifolds with poor spines

A. Yu. Vesninab, V. G. Turaevac, E. A. Fominykhad

a Chelyabinsk State University, Chelyabinsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
c Indiana University Bloomington, Bloomington, IN, USA
d Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: A special spine of a $3$-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev–Viro invariants, we establish that every compact $3$-manifold $M$ with connected nonempty boundary has a finite number of poor special spines. Moreover, all poor special spines of the manifold $M$ have the same number of true vertices. We prove that the complexity of a compact hyperbolic $3$-manifold with totally geodesic boundary that has a poor special spine with two $2$-components and $n$ true vertices is equal to $n$. Such manifolds are constructed for infinitely many values of $n$.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00513, 14-01-00441
Ministry of Education and Science of the Russian Federation НШ-1015.2014.1


DOI: https://doi.org/10.1134/S0371968515010033

Full text: PDF file (209 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 288, 29–38

Bibliographic databases:

UDC: 515.162.3
Received in November 2014

Citation: A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Three-dimensional manifolds with poor spines”, Geometry, topology, and applications, Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 38–48; Proc. Steklov Inst. Math., 288 (2015), 29–38

Citation in format AMSBIB
\Bibitem{VesTurFom15}
\by A.~Yu.~Vesnin, V.~G.~Turaev, E.~A.~Fominykh
\paper Three-dimensional manifolds with poor spines
\inbook Geometry, topology, and applications
\bookinfo Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 288
\pages 38--48
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3608}
\crossref{https://doi.org/10.1134/S0371968515010033}
\elib{http://elibrary.ru/item.asp?id=23302158}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 288
\pages 29--38
\crossref{https://doi.org/10.1134/S0081543815010034}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000353881900003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928739505}


Linking options:
  • http://mi.mathnet.ru/eng/tm3608
  • https://doi.org/10.1134/S0371968515010033
  • http://mi.mathnet.ru/eng/tm/v288/p38

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Sb. Math., 207:11 (2016), 1493–1511  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. Yu. Vesnin, S. V. Matveev, E. A. Fominykh, “New aspects of complexity theory for 3-manifolds”, Russian Math. Surveys, 73:4 (2018), 615–660  mathnet  crossref  crossref  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:289
    Full text:27
    References:33
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020