[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2018.31.1.475

NONABELIAN GROUP ACTIONS ON 3-DIMENSIONAL NILMANIFOLDS REVERSING FIBER ORIENTATION

Koo, Daehwan (Daejeon Science High School for the Gifted)
Lee, Taewoong (Mannyon High School)
Shin, Joonkook (Department of Mathematics Education Chungnam National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.31, no.4, 2018 , pp. 475-486 More about this Journal

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 $C_4/C_2=C_2$ ).

Keywords

affine conjugacy; almost Bieberbach group; group action; Heisenberg group;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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