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Journal of the London Mathematical Society 1998 58(1):229-238; doi:10.1112/S0024610798006231
© 1998 by London Mathematical Society
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© The London Mathematical Society

On 4-Dimensional Mapping Tori and Product Geometries

Jonathan A. Hillman

School of Mathematics and Statistics, University of Sydney Sydney, NSW 2006, Australia

Received 15 June 1995.

The paper gives simple necessary and sufficient conditions for 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. The paper also considers 4-manifolds which admit a geometry of Euclidean factor type and complex surfaces which fibre over S1.


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