Examples of exotic stratifications

Hughes, Bruce¹ ; Taylor, Laurence R² ; Weinberger, Shmuel³ ; Williams, E Bruce²

¹ Department of Mathematics, Vanderbilt University, Nashville TN 37240, USA
² Department of Mathematics, University of Notre Dame, Notre Dame IN 46556, USA
³ Department of Mathematics, University of Chicago, Chicago IL 60637, USA

Geometry & topology, Tome 11 (2007) no. 3, pp. 1477-1505.

Résumé

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.

Détail

DOI : 10.2140/gt.2007.11.1477

Keywords: locally conelike stratified space, manifold approximate fibration

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