On 3-manifolds with locally standard (Z2)3-actions
On 3-manifolds with locally standard (Z2)3-actions
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DOI：
10.1016/j.topol.2013.01.005
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发表时间：
2008-07
影响因子：
0.6
通讯作者：
Zhi Lu;Li Yu
中科院分区：
文献类型：
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作者：
Zhi Lu;Li Yu
我们研究了什么样的闭三维流形可以容纳局部标准作用。特别地，我们将证明，对于H1（M;Z2）=0的闭连通3-流形M，M容许局部标准作用当且仅当M是Z2-同调球面N的8个拷贝的连通和。因此，如果这样的M是不可约的，那么它一定同胚于S3。此外，该论证还可以推广到研究具有H1（M;Z2）<$Z2的可定向有理同调3-球面M，它允许局部标准作用。
We investigate what kind of closed 3-manifolds can admit locally standard [Formula: see text] -actions. In particular, we will prove that for a closed connected 3-manifold M with H1(M;Z2)=0, M admits a locally standard [Formula: see text] -action if and only if M is a connected sum of 8 copies of a Z2-homology sphere N. So if such an M is irreducible, it must be homeomorphic to S3. Moreover, the argument can be extended to study orientable rational homology 3-spheres M with H1(M;Z2)≅Z2which admits locally standard [Formula: see text] -actions.