Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0440577
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57D75

Retrieve articles in all journals with MSC: 57D75

Additional Information

Keywords: Line-element parallelizable manifold
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society