New aspects of complexity theory for 3-manifolds

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

doi:10.1070/RM9829

New aspects of complexity theory for 3-manifolds

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

Faculty of Mathematics and Mechanics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	615-660
Number of pages	46
Journal	Russian Mathematical Surveys
Volume	73
Issue number	4
DOIs	https://doi.org/10.1070/RM9829
State	Published - 1 Aug 2018

Scopus subject areas

Mathematics(all)

Keywords

3-manifolds
Matveev complexity
spines
tetrahedral complexity
triangulations

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10.1070/RM9829

Cite this

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KW - tetrahedral complexity

KW - triangulations

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New aspects of complexity theory for 3-manifolds

Abstract

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Keywords

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