This article is cited in 7 papers

Complexity of 3-dimensional manifolds: exact values and estimates

A. Yu. Vesnin^a, S. V. Matveev^bc, E. A. Fominykh<sup>bc

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^c Chelyabinsk State University

Abstract: The paper is a survey of recent results on the complexity theory of 3-manifolds obtained by the authors and their colleagues. We describe existing tables of closed 3-manifolds and several infinite series of 3-manifolds with known complexities. We also give potentially exact estimates of complexity of Seifert and graph manifolds as well as for large families of hyperbolic manifolds.

Keywords: Matveev's complexity, 3-manifolds.

UDC: 515.162.32

MSC: 57M27, 57M50

Received November 14, 2011, published November 15, 2011