Amenable category of three–manifolds

Gómez-Larrañaga, José Carlos¹ ; González-Acuña, Francisco² ; Heil, Wolfgang³

¹Centro de Investigación en Matemáticas, A.P. 402, 36000 Guanajuato, Mexico
²Instituto de Matemáticas, UNAM Morelos Campus, 62210 Cuernavaca,, Mexico, Centro de Investigación en Matemáticas, A.P. 402, 36000 Guanajuato, Mexico
³Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 905-925

Résumé

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.

Détail

DOI : 10.2140/agt.2013.13.905

Classification : 55M30, 57M27, 57N10, 57N16
Keywords: coverings of $n$–manifolds with amenable subsets, amenable cover of 3–manifolds, Lusternik–Schnirelmann, virtually solvable 3–manifold groups

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