# Stratifications of teardrops

Fundamenta Mathematicae (1999)

- Volume: 161, Issue: 3, page 305-324
- ISSN: 0016-2736

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topHughes, Bruce. "Stratifications of teardrops." Fundamenta Mathematicae 161.3 (1999): 305-324. <http://eudml.org/doc/212408>.

@article{Hughes1999,

abstract = {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.},

author = {Hughes, Bruce},

journal = {Fundamenta Mathematicae},

keywords = {stratified space; teardrop; homotopically stratified space; stratified approximate fibration; mapping cylinder; manifold stratified space},

language = {eng},

number = {3},

pages = {305-324},

title = {Stratifications of teardrops},

url = {http://eudml.org/doc/212408},

volume = {161},

year = {1999},

}

TY - JOUR

AU - Hughes, Bruce

TI - Stratifications of teardrops

JO - Fundamenta Mathematicae

PY - 1999

VL - 161

IS - 3

SP - 305

EP - 324

AB - 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.

LA - eng

KW - stratified space; teardrop; homotopically stratified space; stratified approximate fibration; mapping cylinder; manifold stratified space

UR - http://eudml.org/doc/212408

ER -

## References

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- [12] B. Hughes, L. Taylor and B. Williams, Bundle theories for topological manifolds, Trans. Amer Math. Soc. 319 (1990), 1-65. Zbl0704.57012
- [13] B. Hughes, L. Taylor and B. Williams, Manifold approximate fibrations are approximately bundles, Forum Math. 3 (1991), 309-325. Zbl0728.55009
- [14] B. Hughes and S. Weinberger, Surgery and stratified spaces, preprint, http://xxx.lanl.gov/abs/math.GT/9807156. Zbl0982.57009
- [15] F. Quinn, Homotopically stratified sets, J. Amer. Math. Soc. 1 (1988), 441-499. Zbl0655.57010
- [16] C. Rourke and B. Sanderson, An embedding without a normal bundle, Invent. Math. 3 (1967), 293-299. Zbl0168.44602
- [17] L. Siebenmann, The obstruction to finding a boundary of an open manifold of dimension greater than five, Ph.D. thesis, Princeton Univ., 1965.

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