Geodesic
Finite actions on the Klein four-orbifold and prism manifolds
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 49-68.

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We describe the finite group actions, up to equivalence, which can act on the orbifold $\Sigma(2,2,2)$, and their quotient types. This is then used to consider actions on prism manifolds $M(b,d)$ which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If $\varphi\colon G\rightarrow \text{Homeo} (M(b,d))$ is such an action, we show that $M(b,d) = M(b,2)$ and $M(b,2)/\varphi$ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by $\Sigma(2,2,2)$. For the standard actions, we compute the fundamental group of $M(b,2)/\varphi$ and indicate when it is a Seifert fibered manifold.
DOI : 10.14712/1213-7243.2015.193
Classification : 57M99, 57S99
Keywords: finite group action; prism 3-manifold; equivalence of actions; orbifold; Klein four-group 
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Kalliongis, John; Ohashi, Ryo. Finite actions on the Klein four-orbifold and prism manifolds. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 1, pp. 49-68. doi : 10.14712/1213-7243.2015.193. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.193/

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