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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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참고문헌 (4)
참고문헌 신청
최동순 / 2005 / Free actions of finite abelian groups on 3-dimensional nilmanifolds / 대한수학회지 42(4):795~826
K. Dekimpe / 1995 / Affine structures for closed 3-dimensional manifolds with nil-geometry / Quarterly J. Math 46(2):141~167
구대환 / 2017 / CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS / 대한수학회지 54(5):1411~1440
F. Waldhausen / 1968 / On irreducible 3-manifolds which are sufficiently large / Ann. of Math 87(2):56~88
K. Dekimpe / 1995 / Affine structures for closed 3-dimensional manifolds with nil-geometry / Quarterly J. Math 46(2):141~167
구대환 / 2017 / CLASSIFICATION OF FREE ACTIONS OF FINITE GROUPS ON 3-DIMENSIONAL NILMANIFOLDS / 대한수학회지 54(5):1411~1440
F. Waldhausen / 1968 / On irreducible 3-manifolds which are sufficiently large / Ann. of Math 87(2):56~88
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