Algebraic and Geometric Topology 5 (2005), paper no. 43, pages 1051-1073.

Non-singular graph-manifolds of dimension 4

A. Mozgova

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

AMS subject classification. Primary: 57M50, 57N35.

E-print: arXiv:math.GT/0411335

DOI: 10.2140/agt.2005.5.1051

Submitted: 29 March 2005. (Revised: 30 July 2005.) Accepted: 4 August 2005. Published: 29 August 2005.

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A. Mozgova
Laboratoire d'analyse non lineaire et geometrie, Universite d'Avignon
33, rue Louis Pasteur, 84000 Avignon, France, and
Laboratoire Emile Picard, UMP 5580, Universite Paul Sabatier
118, route de Narbonne, 31062 Toulouse, France

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