Teardrops are generalizations of open mapping cylinders. We prove that the teardrop of a stratified approximate fibration X → Y × ℝ with X and Y homotopically stratified spaces is itself a homotopically stratified space (under mild hypothesis). This is applied to manifold stratified approximate fibrations between manifold stratified spaces in order to establish the realization part of a previously announced tubular neighborhood theory.
@article{bwmeta1.element.bwnjournal-article-fmv161i3p305bwm,
author = {Bruce Hughes},
title = {Stratifications of teardrops},
journal = {Fundamenta Mathematicae},
volume = {159},
year = {1999},
pages = {305-324},
zbl = {0942.57021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p305bwm}
}
Hughes, Bruce. Stratifications of teardrops. Fundamenta Mathematicae, Tome 159 (1999) pp. 305-324. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv161i3p305bwm/
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