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 | References | Similar Articles | Additional Information
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.
- Denis Sjerve, Geometric dimension of vector bundles over lens spaces, Trans. Amer. Math. Soc. 134 (1968), 545–557. MR 233373, DOI https://doi.org/10.1090/S0002-9947-1968-0233373-X
- Toshio Yoshida, A remark on vector fields on lens spaces, J. Sci. Hiroshima Univ. Ser. A-I Math. 31 (1967), 13–15. MR 216516
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Keywords:
Lens space,
linearly independent vector field,
associated principal bundle
Article copyright:
© Copyright 1970
American Mathematical Society