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Proceedings of the American Mathematical Society

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

 
 

 

Orientable line-element parallelizable manifolds


Author: R. Michael Alliston
Journal: Proc. Amer. Math. Soc. 63 (1977), 348-352
MSC: Primary 57D75
DOI: https://doi.org/10.1090/S0002-9939-1977-0440577-0
MathSciNet review: 0440577
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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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DOI: https://doi.org/10.1090/S0002-9939-1977-0440577-0
Keywords: Line-element parallelizable manifold
Article copyright: © Copyright 1977 American Mathematical Society

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