On fibering and splitting of 5-manifolds over the circle

Details On fibering and splitting of 5-manifolds over the circle On fibering and splitting of 5-manifolds over the circle

2007-12-10

arxiv.org/abs/0712.1583v2

Topology and its Applications, Volume 156, Number 2 (2008), 284--299

Mathematics

Geometric Topology

22 pages, exposition revised for better self-containment

Scientific paper

10.1016/j.topol.2008.07.007

Our main result is a generalization of Cappell's 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For example, these maps may have homotopy fibers which are in the class of finite connected sums of certain geometric 4-manifolds. Most of these homotopy fibers have non-vanishing second mod 2 homology and have fundamental groups of exponential growth, which are not known to be tractable by Freedman--Quinn topological surgery. Indeed, our key technique is topological cobordism, which may not be the trace of surgeries.

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