We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane reflections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.
SOME HYPERBOLIC SPACE FORMS WITH FEW GENERATED FUNDAMENTAL GROUPS / Cavicchioli, Alberto; Emil, Molnar; Agnese I., Telloni. - In: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY. - ISSN 0304-9914. - STAMPA. - 50:2(2013), pp. 425-444. [10.4134/JKMS.2013.50.2.425]
SOME HYPERBOLIC SPACE FORMS WITH FEW GENERATED FUNDAMENTAL GROUPS
CAVICCHIOLI, Alberto;
2013
Abstract
We construct some hyperbolic hyperelliptic space forms whose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extended Coxeter group generated by plane reflections and half-turns. Then we describe covering properties and determine the isometry groups of the constructed manifolds. Furthermore, we give an explicit construction of space form of the second smallest volume nonorientable hyperbolic 3-manifold with one cusp.
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