Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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NONABELIAN GROUP ACTIONS ON 3-DIMENSIONAL NILMANIFOLDS REVERSING FIBER ORIENTATION

  • Received : 2018.10.17
  • Accepted : 2018.11.05
  • Published : 2018.11.15
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Abstract

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\bigoplus}{\mathbb{Z}}_2$ which yield an orbit manifold reversing fiber orientation, up to topological conjugacy. We show that those nonabelian groups are $D_4$(the dihedral group), $Q_8$(the quaternion group), and $C_8.C_4$(the $1^{st}$ non-split extension by $C_8$ of $C_4$ acting via $C_4/C_2=C_2$).

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References

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