Geometry & Topology
- Geom. Topol.
- Volume 11, Number 3 (2007), 1477-1505.
Examples of exotic stratifications
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.
Geom. Topol., Volume 11, Number 3 (2007), 1477-1505.
Revised: 31 May 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57N80: Stratifications
Secondary: 19J99: None of the above, but in this section 55R65: Generalizations of fiber spaces and bundles 57N55: Microbundles and block bundles [See also 55R60, 57Q50]
Hughes, Bruce; Taylor, Laurence R; Weinberger, Shmuel; Williams, E Bruce. Examples of exotic stratifications. Geom. Topol. 11 (2007), no. 3, 1477--1505. doi:10.2140/gt.2007.11.1477. https://projecteuclid.org/euclid.gt/1513799900