Volume 11, issue 3 (2007)

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Examples of exotic stratifications

Bruce Hughes, Laurence R Taylor, Shmuel Weinberger and Bruce Williams

Geometry & Topology 11 (2007) 1477–1505

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.

locally conelike stratified space, manifold approximate fibration
Mathematical Subject Classification 2000
Primary: 57N80
Secondary: 19J99, 55R65, 57N55
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Revised: 31 May 2007
Published: 23 July 2007
Proposed: Steve Ferry
Seconded: Rob Kirby and Wolfgang Lueck
Bruce Hughes
Department of Mathematics
Vanderbilt University
Nashville TN 37240
Laurence R Taylor
Department of Mathematics
University of Notre Dame
Notre Dame IN 46556
Shmuel Weinberger
Department of Mathematics
University of Chicago
Chicago IL 60637
Bruce Williams
Department of Mathematics
University of Notre Dame
Notre Dame IN 46556