RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2016, Volume 207, Number 11, Pages 4–24 (Mi msb8700)  

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

Complexity of virtual 3-manifolds

A. Yu. Vesninab, V. G. Turaevcb, E. A. Fominykhbd

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

Abstract: Virtual $3$-manifolds were introduced by Matveev in 2009 as natural generalizations of classical $3$-manifolds. In this paper, we introduce a notion of complexity for a virtual $3$-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two $2$-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic $3$-manifolds with totally geodesic boundary.
Bibliography: 24 titles.

Keywords: virtual manifolds, $3$-manifolds, hyperbolic manifolds, complexity.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0020
1.1260.2014/K
Russian Foundation for Basic Research 16-01-00609-a
This work was supported by the Laboratory of Quantum Topology, Chelyabinsk State University (grant no. 14.Z50.31.0020 of the government of the Russian Federation). A. Yu. Vesnin and E. A. Fominykh were also supported in part by the Russian Foundation for Basic Research (grant no. 16-01-00609-a), and by the Ministry of Education and Science of the Russian Federation (state task no. 1.1260.2014/K).


DOI: https://doi.org/10.4213/sm8700

Full text: PDF file (858 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2016, 207:11, 1493–1511

Bibliographic databases:

Document Type: Article
UDC: 515.16
MSC: Primary 57M99; Secondary 57M20
Received: 20.03.2016

Citation: A. Yu. Vesnin, V. G. Turaev, E. A. Fominykh, “Complexity of virtual 3-manifolds”, Mat. Sb., 207:11 (2016), 4–24; Sb. Math., 207:11 (2016), 1493–1511

Citation in format AMSBIB
\Bibitem{VesTurFom16}
\by A.~Yu.~Vesnin, V.~G.~Turaev, E.~A.~Fominykh
\paper Complexity of virtual 3-manifolds
\jour Mat. Sb.
\yr 2016
\vol 207
\issue 11
\pages 4--24
\mathnet{http://mi.mathnet.ru/msb8700}
\crossref{https://doi.org/10.4213/sm8700}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3588977}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016SbMat.207.1493V}
\elib{http://elibrary.ru/item.asp?id=27350057}
\transl
\jour Sb. Math.
\yr 2016
\vol 207
\issue 11
\pages 1493--1511
\crossref{https://doi.org/10.1070/SM8700}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000393619200001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85011586027}


Linking options:
  • http://mi.mathnet.ru/eng/msb8700
  • https://doi.org/10.4213/sm8700
  • http://mi.mathnet.ru/eng/msb/v207/i11/p4

    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. E. A. Sbrodova, V. V. Tarkaev, E. A. Fominykh, E. V. Shumakova, “Virtualnye trekhmernye mnogoobraziya slozhnosti $1$$2$”, Tr. IMM UrO RAN, 23, no. 4, 2017, 257–264  mathnet  crossref  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
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:389
    References:35
    First page:47

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019