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1999 | 161 | 3 | 305-324
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Stratifications of teardrops

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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.
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Bibliografia
  • [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.
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bwmeta1.element.bwnjournal-article-fmv161i3p305bwm
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