Finite actions on the Klein four-orbifold and prism manifolds
Commentationes Mathematicae Universitatis Carolinae (2017)
- Volume: 58, Issue: 1, page 49-68
- ISSN: 0010-2628
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topKalliongis, John, and Ohashi, Ryo. "Finite actions on the Klein four-orbifold and prism manifolds." Commentationes Mathematicae Universitatis Carolinae 58.1 (2017): 49-68. <http://eudml.org/doc/287895>.
@article{Kalliongis2017,
abstract = {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.},
author = {Kalliongis, John, Ohashi, Ryo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {finite group action; prism 3-manifold; equivalence of actions; orbifold; Klein four-group},
language = {eng},
number = {1},
pages = {49-68},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Finite actions on the Klein four-orbifold and prism manifolds},
url = {http://eudml.org/doc/287895},
volume = {58},
year = {2017},
}
TY - JOUR
AU - Kalliongis, John
AU - Ohashi, Ryo
TI - Finite actions on the Klein four-orbifold and prism manifolds
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 1
SP - 49
EP - 68
AB - 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.
LA - eng
KW - finite group action; prism 3-manifold; equivalence of actions; orbifold; Klein four-group
UR - http://eudml.org/doc/287895
ER -
References
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