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Piecewise linear bundles in the metastable range


Author: Kenneth C. Millett
Journal: Trans. Amer. Math. Soc. 216 (1976), 337-350
MSC: Primary 57C50
DOI: https://doi.org/10.1090/S0002-9947-1976-0423361-7
MathSciNet review: 0423361
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Abstract: For numerable vector bundles a nonzero section determines a unique trivial line subbundle containing the section and this subbundle is a direct summand of the bundle. The main result, a consequence of concordance-isotopy theory, states that in the metastable range a nonzero section to a piecewise linear $ {{\mathbf{R}}^n}$ bundle determines a unique trivial line subbundle and that this is the best possible result. This fact is then compared with the known failure of the summand property below the stable range.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0423361-7
Keywords: Nonzero sections, piecewise linear bundles, trivial subbundles, space of piecewise linear embeddings, concordances, isotopies
Article copyright: © Copyright 1976 American Mathematical Society

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