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Proceedings of the American Mathematical Society

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

 
 

 

Span of lens spaces


Author: Kôichi Iwata
Journal: Proc. Amer. Math. Soc. 26 (1970), 687-688
MSC: Primary 57.34
DOI: https://doi.org/10.1090/S0002-9939-1970-0267600-4
MathSciNet review: 0267600
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Abstract: We prove that the span (i.e., maximal number of linearly independent vector fields) of $ (2n + 1)$-dimensional lens spaces $ {L^n}(p)$, where $ p$ is an odd prime and where $ n + 1 = m \cdot {2^t}$ ($ m$ odd), is equal to the span of $ (2n + 1)$-dimensional sphere if $ t + 1 \equiv 0,1,2\pmod 4$ or if $ n > 3,t + 1 \equiv 3\pmod 4$, and $ p \geqq t + 3$. This result is an improvement of a theorem given by T. Yoshida.


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

  • [1] Denis Sjerve, Geometric dimension of vector bundles over lens spaces, Trans. Amer. Math. Soc. 134 (1968), 545-557. MR 38 #1695. MR 0233373 (38:1695)
  • [2] Toshio Yoshida, A remark on vector fields on lens spaces, J. Sci. Hiroshima Univ. Ser. A-I Math. 31 (1967), 13-15. MR 35 #7349. MR 0216516 (35:7349)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0267600-4
Keywords: Lens space, linearly independent vector field, associated principal bundle
Article copyright: © Copyright 1970 American Mathematical Society

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