Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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.)
  • Received : 2012.06.26
  • Published : 2013.03.01
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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.

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References

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