Volume 5, issue 3 (2005)

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Non-singular graph-manifolds of dimension 4

A Mozgova

Algebraic & Geometric Topology 5 (2005) 1051–1073
 arXiv: math.GT/0411335
Abstract

A compact $4$–dimensional manifold is a non-singular graph-manifold if it can be obtained by the glueing ${T}^{2}$–bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the bundle structures, the graph-structure is called reduced. We prove that any homotopy equivalence of closed oriented $4$–manifolds with reduced nonsingular graph-structures is homotopic to a diffeomorphism preserving the structures.

Keywords
graph-manifold, $\pi_1$–injective submanifold
Mathematical Subject Classification 2000
Primary: 57M50, 57N35
Publication
Received: 29 March 2005
Revised: 30 July 2005
Accepted: 4 August 2005
Published: 29 August 2005
Authors
 A Mozgova Laboratoire d’analyse non linéaire et géométrie Université d’Avignon 33, rue Louis Pasteur 84000 Avignon France Laboratoire Emile Picard UMP 5580 Université Paul Sabatier 118, route de Narbonne 31062 Toulouse France