Finite actions on the Klein four-orbifold and prism manifolds

[摘要] 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.

[学科分类] 物理化学和理论化学

[关键词] finite group action;prism 3-manifold;equivalence of actions;orbifold;Klein four-groupDOI: DOI 10.14712/1213-7243.2015.193AMS Subject Classification: 57M99 57S99 PDF