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ArticleOriginal scientific text

Title

Stratifications of teardrops

Authors 1

Affiliations

  1. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, U.S.A.

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.

Keywords

ENG
stratified space, teardrop, homotopically stratified space, stratified approximate fibration, mapping cylinder, manifold stratified space

Bibliography

  1. A. Beshears, G-isovariant structure sets and stratified structure sets, Ph.D. thesis, Vanderbilt Univ., 1997.
  2. T. A. Chapman, Approximation results in topological manifolds, Mem. Amer. Math. Soc. 251 (1981).
  3. D. Coram and P. Duvall, Approximate fibrations, Rocky Mountain J. Math. 7 (1977), 275-288.
  4. R. D. Edwards, TOP regular neighborhoods, handwritten manuscript, 1973.
  5. B. Hughes, Approximate fibrations on topological manifolds, Michigan Math. J. 32 (1985), 167-183.
  6. B. Hughes, Geometric topology of stratified spaces, Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 73-81.
  7. B. Hughes, Stratified path spaces and fibrations, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), 351-384.
  8. B. Hughes, Stratifications of mapping cylinders, Topology Appl. 94 (1999), 127-145.
  9. B. Hughes, The geometric topology of stratified spaces, in preparation.
  10. B. Hughes and A. Ranicki, Ends of Complexes, Cambridge Tracts in Math. 123, Cambridge Univ. Press, Cambridge, 1996.
  11. B. Hughes, L. Taylor, S. Weinberger and B. Williams, Neighborhoods in stratified spaces with two strata, Topology, to appear.
  12. B. Hughes, L. Taylor and B. Williams, Bundle theories for topological manifolds, Trans. Amer Math. Soc. 319 (1990), 1-65.
  13. B. Hughes, L. Taylor and B. Williams, Manifold approximate fibrations are approximately bundles, Forum Math. 3 (1991), 309-325.
  14. B. Hughes and S. Weinberger, Surgery and stratified spaces, preprint, http://xxx.lanl.gov/abs/math.GT/9807156.
  15. F. Quinn, Homotopically stratified sets, J. Amer. Math. Soc. 1 (1988), 441-499.
  16. C. Rourke and B. Sanderson, An embedding without a normal bundle, Invent. Math. 3 (1967), 293-299.
  17. L. Siebenmann, The obstruction to finding a boundary of an open manifold of dimension greater than five, Ph.D. thesis, Princeton Univ., 1965.
Fundamenta Mathematicae
1999/161/3
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Pages:
305-324
Main language of publication
English
Received
1998-09-19
Published
1999
Exact and natural sciences