On 4-dimensional mapping tori and product geometries


Jonathan A. Hillman


Research Report 94-14, 1 May 1994


We give simple necessary and sufficient conditions for an infinite cyclic covering space of a closed 4-manifold to be homotopy equivalent to the mapping torus of a self homotopy equivalence of a PD3-complex. This is a homotopy analogue of the Stallings and Farrell fibration theorems available in other dimensions. We consider also 4-manifolds which admit a geometry of euclidean factor type.

Key phrases

4-manifold. geometry. mapping torus.

AMS Subject Classification (1991)

Primary: 57N13
Secondary: 55R10, 53C30


The paper is available in the following forms:
TeX dvi format:
map-tori.dvi.gz (15kB) or map-tori.dvi (35kB)

map-tori.ps.gz (36kB) or map-tori.ps (120kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics