Volume 13, issue 2 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Amenable category of three–manifolds

José Carlos Gómez-Larrañaga, Francisco González-Acuña and Wolfgang Heil

Algebraic & Geometric Topology 13 (2013) 905–925
Abstract

A closed topological n–manifold Mn is of ame–category k if it can be covered by k open subsets such that for each path-component W of the subsets the image of its fundamental group π1(W) π1(Mn) is an amenable group. catame(Mn) is the smallest number k such that Mn admits such a covering. For n = 3, M3 has ame–category 4. We characterize all closed 3–manifolds of ame–category 1, 2 and 3.

Keywords
coverings of $n$–manifolds with amenable subsets, amenable cover of 3–manifolds, Lusternik–Schnirelmann, virtually solvable 3–manifold groups
Mathematical Subject Classification 2010
Primary: 55M30, 57M27, 57N10
Secondary: 57N16
References
Publication
Received: 31 August 2011
Revised: 23 October 2012
Accepted: 2 November 2012
Published: 30 March 2013
Authors
José Carlos Gómez-Larrañaga
Centro de Investigación en Matemáticas
A.P. 402
36000 Guanajuato
Mexico
Francisco González-Acuña
Instituto de Matemáticas
UNAM Morelos Campus
62210 Cuernavaca,
Mexico
Centro de Investigación en Matemáticas
A.P. 402
36000 Guanajuato
Mexico
Wolfgang Heil
Department of Mathematics
Florida State University
Tallahassee, FL 32306-4510
USA
http://www.math.fsu.edu/People/faculty.php?id=16