Orientable line-element parallelizable manifolds

Alliston, R. Michael

doi:10.1090/S0002-9939-1977-0440577-0

Orientable line-element parallelizable manifolds
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by R. Michael Alliston PDF

Proc. Amer. Math. Soc. 63 (1977), 348-352 Request permission

Abstract:

Examples of oriented, nonbounding, line-element parallelizable manifolds are given in all odd dimensions $n \ne 5$ or ${2^r} - 1$. Furthermore, these examples are indecomposable in the unoriented bordism ring, and hence represent generators of $\operatorname {Tor} \;{\Omega _\ast }$, the torsion subgroup of the oriented bordism ring. It is also proven that every class of $\operatorname {Tor} \;{\Omega _\ast }$ admits a representative M such that $\tau (M) \oplus 2$ splits as a sum of line bundles over M.

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