Stratifications of teardrops

Bruce Hughes

Fundamenta Mathematicae (1999)

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

Abstract

top
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.

How to cite

top

Hughes, 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

top
  1. [1] A. Beshears, G-isovariant structure sets and stratified structure sets, Ph.D. thesis, Vanderbilt Univ., 1997. 
  2. [2] T. A. Chapman, Approximation results in topological manifolds, Mem. Amer. Math. Soc. 251 (1981). Zbl0478.57009
  3. [3] D. Coram and P. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), 275-288. Zbl0367.55019
  4. [4] R. D. Edwards, TOP regular neighborhoods, handwritten manuscript, 1973. 
  5. [5] B. Hughes, Approximate fibrations on topological manifolds, Michigan Math. J. 32 (1985), 167-183. Zbl0575.55014
  6. [6] B. Hughes, Geometric topology of stratified spaces, Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 73-81. Zbl0866.57018
  7. [7] B. Hughes, Stratified path spaces and fibrations, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), 351-384. Zbl0923.55007
  8. [8] B. Hughes, Stratifications of mapping cylinders, Topology Appl. 94 (1999), 127-145. Zbl0928.57027
  9. [9] B. Hughes, The geometric topology of stratified spaces, in preparation. Zbl0866.57018
  10. [10] B. Hughes and A. Ranicki, Ends of Complexes, Cambridge Tracts in Math. 123, Cambridge Univ. Press, Cambridge, 1996. Zbl0876.57001
  11. [11] B. Hughes, L. Taylor, S. Weinberger and B. Williams, Neighborhoods in stratified spaces with two strata, Topology, to appear. Zbl0954.57008
  12. [12] B. Hughes, L. Taylor and B. Williams, Bundle theories for topological manifolds, Trans. Amer Math. Soc. 319 (1990), 1-65. Zbl0704.57012
  13. [13] B. Hughes, L. Taylor and B. Williams, Manifold approximate fibrations are approximately bundles, Forum Math. 3 (1991), 309-325. Zbl0728.55009
  14. [14] B. Hughes and S. Weinberger, Surgery and stratified spaces, preprint, http://xxx.lanl.gov/abs/math.GT/9807156. Zbl0982.57009
  15. [15] F. Quinn, Homotopically stratified sets, J. Amer. Math. Soc. 1 (1988), 441-499. Zbl0655.57010
  16. [16] C. Rourke and B. Sanderson, An embedding without a normal bundle, Invent. Math. 3 (1967), 293-299. Zbl0168.44602
  17. [17] L. Siebenmann, The obstruction to finding a boundary of an open manifold of dimension greater than five, Ph.D. thesis, Princeton Univ., 1965. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.