Volume 5, issue 3 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 T2–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