New aspects of complexity theory for 3-manifolds

A. Yu Vesnin, S. V. Matveev, E. A. Fominykh

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)615-660
Number of pages46
JournalRussian Mathematical Surveys
Issue number4
StatePublished - 1 Aug 2018

Scopus subject areas

  • Mathematics(all)


  • 3-manifolds
  • Matveev complexity
  • spines
  • tetrahedral complexity
  • triangulations


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