Geodesic
Stratifications of teardrops
Fundamenta Mathematicae, Tome 161 (1999) no. 3, pp. 305-324
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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.
DOI : 10.4064/fm-161-3-305-324
Keywords: stratified space, teardrop, homotopically stratified space, stratified approximate fibration, mapping cylinder, manifold stratified space 
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Bruce Hughes. Stratifications of teardrops. Fundamenta Mathematicae, Tome 161 (1999) no. 3, pp. 305-324. doi: 10.4064/fm-161-3-305-324

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