On closed $\delta$-pinched manifolds with discrete abelian group actions
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- by Yusheng Wang
- Proc. Amer. Math. Soc. 137 (2009), 265-272
- DOI: https://doi.org/10.1090/S0002-9939-08-09454-9
- Published electronically: July 28, 2008
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Abstract:
Let $M^{n}$ be a closed odd $n$-manifold with sectional curvature $\delta <\sec _{M}\le 1$, and let $M$ admit an effective isometric $\mathbb {Z}^{k}_{p}$-action with $p$ prime. The main results in the paper are: (1) if $\delta >0$ and $n\ge 5$, then there exists a constant $p(n,\delta )$, depending only on $n$ and $\delta$, such that $p\ge p(n,\delta )$ implies that (i) $k\le \frac {n+1}{2}$, (ii) the universal covering space of $M$ is homeomorphic to $S^{n}$ if $k>\frac {3}{8}n+1$, (iii) the fundamental group $\pi _{1}(M)$ is cyclic if $k>\frac {n+1}{4}+1$; (2) if $\delta =0$ and $n=3$, then $k\le 4$ for $p=2$ and $k\le 2$ for $p\ge 3$, and $\pi _{1}(M)$ is cyclic if $p\ge 5$ and $k=2$.References
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Bibliographic Information
- Yusheng Wang
- Affiliation: School of Mathematical Sciences (& Lab. Math. Com. Sys.), Beijing Normal University, Beijing 100875, People’s Republic of China
- Email: wyusheng@163.com, wwyusheng@gmail.com
- Received by editor(s): December 20, 2006
- Received by editor(s) in revised form: December 12, 2007
- Published electronically: July 28, 2008
- Additional Notes: The author was supported in part by NSFC Grant #10671018.
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 265-272
- MSC (2000): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-08-09454-9
- MathSciNet review: 2439449