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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Bundles along the fiber in the PL category


Author: Norman Levitt
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0915747-2
Keywords: Vector bundle, PL-disk bundle, PL-sphere bundle, bundle of tangents along the fiber, bundle of $ k$-frames
Article copyright: © Copyright 1988 American Mathematical Society