Geometrically Finite Groups

  • Bernard Maskit
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 287)


This chapter is an exploration of geometrically finite discrete subgroups of M; that is, groups that have (convex) fundamental polyhedra in ℍ3 with finitely many sides. One of our main objectives is to give a criterion for a group to be geometrically finite in terms of its action at the limit set; this criterion will then be used in Chapter VII to show that, under suitable conditions, the combination of two geometrically finite groups is again geometrically finite.


Finite Group Limit Point Distinct Element Parabolic Subgroup Discrete Subgroup 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Bernard Maskit
    • 1
  1. 1.Dept. of MathematicsSUNY at Stony BrookStony BrookUSA

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