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Russian Mathematical Surveys, 2018, Volume 73, Issue 4, Pages 615–660
DOI: https://doi.org/10.1070/RM9829 (Mi rm9829) 		 
This article is cited in 3 scientific papers (total in 3 papers)

New aspects of complexity theory for 3-manifolds

A. Yu. Vesninab, S. V. Matveevcd, E. A. Fominykhcd

a Tomsk State University
b S. L. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
c Chelyabinsk State University
d N. N. Krasovskii Institute of Mathematics and Mechanics of Russian Academy of Sciences
English version PDF (1124 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/RM9829
Abstract: Recent developments in the theory of complexity for three-dimensional manifolds are reviewed, including results and methods that emerged over the last decade. Infinite families of closed orientable manifolds and hyperbolic manifolds with totally geodesic boundary are presented, and the exact values of the Matveev complexity are given for them. New methods for computing complexity are described, based on calculation of the Turaev–Viro invariants and hyperbolic volumes of 3-manifolds.
Bibliography: 89 titles.
Keywords: 3-manifolds, Matveev complexity, tetrahedral complexity, triangulations, spines.
Funding agency Grant number
Russian Science Foundation 16-11-10291
This research was supported by the Russian Science Foundation under project no. 16-11-10291.
Received: 09.04.2018
Bibliographic databases:
Document Type: Article
UDC: 515.162
MSC: 57M27
Language: English
Original paper language: Russian
Citation: 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
Citation in format AMSBIB
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\paper New aspects of complexity theory for 3-manifolds
\jour Russian Math. Surveys
\yr 2018
\vol 73
\issue 4
\pages 615--660
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Linking options:
  • https://www.mathnet.ru/eng/rm9829
  • https://doi.org/10.1070/RM9829
  • https://www.mathnet.ru/eng/rm/v73/i4/p53
    • This publication is cited in the following 3 articles:
    1. D. D. Nigomedyanov, E. A. Fominykh, “$\beta_1$-Triangulyatsii 3-mnogoobrazii”, Matem. zametki, 117:4 (2025), 630–634  mathnet  crossref
    2. A. Cattabriga, M. Mulazzani, “The complexity of orientable graph manifolds”, Adv. Geom., 22:1 (2022), 113–126  crossref  mathscinet  isi
    3. S. V. Matveev, V. V. Tarkaev, “Recognition and tabulation of $3$-manifolds up to complexity $13$”, Chebyshevskii sb., 21:2 (2020), 290–300  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Statistics & downloads:
    Abstract page:793
    Russian version PDF:166
    English version PDF:75
    References:89
    First page:57
     
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