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Stratified path spaces and fibrations

Published online by Cambridge University Press:  14 November 2011

Bruce Hughes
Bruce Hughes
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, USA, ([email protected])
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Abstract

The main objects of study are the homotopically stratified metric spaces introduced by Quinn. Closed unions of strata are shown to be stratified forward tame. Stratified fibrations between spaces with stratifications are introduced. Paths that lie in a single stratum, except possibly at their initial points, form a space with a natural stratification, and the evaluation map from that space of paths is shown to be a stratified fibration. Applications to mapping cylinders and to the geometry of manifold stratified spaces are expected in future papers.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 2 , 1999 , pp. 351 - 384
Copyright
Copyright © Royal Society of Edinburgh 1999

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