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http://dx.doi.org/10.4134/JKMS.2013.50.2.425

SOME HYPERBOLIC SPACE FORMS WITH FEW GENERATED FUNDAMENTAL GROUPS  

Cavicchioli, Alberto (Dipartimento di Matematica Universita di Modena e Reggio E.)
Molnar, Emil (Department of Geometry Institute of Mathematics Budapest University of Technology and Economics)
Telloni, Agnese I. (Dipartimento di Matematica Universita di Modena e Reggio E.)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 425-444 More about this Journal
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 re ections 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.
Keywords
hyperbolic 3-manifold; hyperelliptic involution; cyclic branched covering; Heegaard diagram; hyperbolic orbifold; fundamental group; isometry group;
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