Qayum Khan
Published 2007-12-10, updated 2008-06-04Version 2
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.
Comments: 22 pages, exposition revised for better self-containment
Journal: Topology and its Applications, Volume 156, Number 2 (2008), 284--299
On fundamental groups of spaces of (framed) embeddings of the circle in a $4$-manifold
The Groups $G_{n}^{k}$ and Fundamental Groups of Configuration Spaces
Quantum deformations of fundamental groups of oriented 3-manifolds
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