Non-singular graph-manifolds of dimension 4

Mozgova, A

doi:10.2140/agt.2005.5.1051

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Non-singular graph-manifolds of dimension 4

A Mozgova

Algebraic & Geometric Topology 5 (2005) 1051–1073

DOI: 10.2140/agt.2005.5.1051

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

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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

Volume 5, issue 3 (2005)