#### 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