## Geometry & Topology

### Examples of exotic stratifications

#### 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.

#### Article information

Source
Geom. Topol., Volume 11, Number 3 (2007), 1477-1505.

Dates
Revised: 31 May 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799900

Digital Object Identifier
doi:10.2140/gt.2007.11.1477

Mathematical Reviews number (MathSciNet)
MR2326949

Zentralblatt MATH identifier
1136.57012

#### Citation

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

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