Bundles along the fiber in the PL category
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- by Norman Levitt PDF
- Proc. Amer. Math. Soc. 102 (1988), 213-217 Request permission
Abstract:
We show that the notion of the bundle of tangents along the fiber over the total space of a fibering is not a good one when the fibering in question is PL. In particular it is shown that there are vector bundles over the same base space such that (1) the associated sphere bundles are PL-equivalent; (2) the consequent homeomorphism of total spaces is not covered by any PL-disk bundle equivalence of the respective bundles of tangents to the fiber manifolds.References
- A. Haefliger and C. T. C. Wall, Piecewise linear bundles in the stable range, Topology 4 (1965), 209–214. MR 184243, DOI 10.1016/0040-9383(65)90007-8
- J. M. Kister, Microbundles are fibre bundles, Ann. of Math. (2) 80 (1964), 190–199. MR 180986, DOI 10.2307/1970498
- R. C. Kirby and L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749. MR 242166, DOI 10.1090/S0002-9904-1969-12271-8
- J. Milnor, Topological manifolds and smooth manifolds, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 132–138. MR 0161345
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 213-217
- MSC: Primary 55R25,; Secondary 55R60
- DOI: https://doi.org/10.1090/S0002-9939-1988-0915747-2
- MathSciNet review: 915747