# On 4-manifolds which admit geometric decompositions or which are Seifert fibred

## Author

**Jonathan A. Hillman**

## Status

Research Report 94-35

28 October 1994

## Abstract

We show that a closed 4-manifold which admits a finite decomposition into geometric
pieces of finite volume is (essentially) either geometric or aspherical.
We also consider the homotopy types of closed 4-manifolds which are Seifert fibred or
which are the total spaces of bundles with base and fibre closed aspherical surfaces.

## Key phrases

4-manifold. geometry. Seifert fibration. surface bundle.

## AMS Subject Classification (1991)

Primary: 57N13

Secondary: 53C30

## Content

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Sydney Mathematics and Statistics