On stability of 3-manifolds
Volume 182 / 2004
Fundamenta Mathematicae 182 (2004), 169-180
MSC: Primary 58R80, 57S25.
DOI: 10.4064/fm182-2-6
Abstract
We address the following question: How different can closed, oriented $3$-manifolds be if they become homeomorphic after taking a product with a sphere?
For geometric $3$-manifolds this paper provides a complete answer to this question. For possibly non-geometric $3$-manifolds, we establish results which concern $3$-manifolds with finite fundamental group (i.e., $3$-dimensional fake spherical space forms) and compare these results with results involving fake spherical space forms of higher dimensions.
