Piecewise linear bundles in the metastable range

Millett, Kenneth C.

doi:10.1090/S0002-9947-1976-0423361-7

Piecewise linear bundles in the metastable range
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Trans. Amer. Math. Soc. 216 (1976), 337-350 Request permission

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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