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NEIGHBORHOODS OF STRATA IN MANIFOLD STRATIFIED SPACES

Published online by Cambridge University Press:  15 January 2004

BRUCE HUGHES
BRUCE HUGHES
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240 e-mail: bruce.hughes@vanderbilt.edu
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Abstract

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Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in manifold stratified spaces, and to spaces of manifold stratified approximate fibrations.

Keywords

Primary 57N8057N40Secondary 55R6558A35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 1 , January 2004 , pp. 1 - 28
Copyright
2004 Glasgow Mathematical Journal Trust

Footnotes

Supported in part by NSF Grant DMS-9971367.