Geometry & Topology 11 (2007) 1477–1505

DOI: 10.2140/gt.2007.11.1477

Abstract

We produce examples of manifold stratified pairs in which the lower strata do not have neighborhoods that are mapping cylinders of fiber bundles, or even block bundles. Moreover, the examples do not improve in this regard under stabilization by products with tori. The examples are locally conelike and the lower strata do have neighborhoods which are mapping cylinders of manifold approximate fibrations. They are constructed by combining the classification of manifold approximate fibrations with the authors’ classification of neighborhood germs.

Keywords

locally conelike stratified space, manifold approximate fibration

Mathematical Subject Classification

Primary: 57N80

Secondary: 19J99, 55R65, 57N55

References

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Publication

Received: 2003
Revised: 31 May 2007
Accepted: 2006
Published: 23 July 2007
Proposed: Steve Ferry
Seconded: Rob Kirby, Wolfgang Lueck

Authors