This article is cited in 3 papers

New aspects of complexity theory for 3-manifolds

A. Yu. Vesnin^ab, S. V. Matveev^cd, E. A. Fominykh<sup>cd

a</sup> 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

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.

UDC: 515.162

MSC: 57M27

Received: 09.04.2018

DOI: 10.4213/rm9829

 English version: Russian Mathematical Surveys, 2018, 73:4, 615–660

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