Geometry of Hyperbolic Space

  • Michael Kapovich
Part of the Modern Birkhäuser Classics book series (MBC)


If G is a group acting on a set X, then for each g ϵ G we let Fix X(g) denote the fixed-point set for the action of g on X and FixX(G) the subset of X fixed by the whole group G (pointwise). Sometimes we shall omit the subscript X in this notation when it is clear what the space X is. If Y ⊂ X is a subset, then we will use the notation FixG(Y) to denote the collection of elements g ϵ G that fix Y pointwise. A sequence x n in a topological space X (i.e., each subsequence in {x n } contains a convergent subsequence). We will say that x n subconverges to x ϵ X if x is the limit of a subsequence in {x n }.


Hyperbolic Space Cayley Graph Hausdorff Distance Geodesic Segment Ideal Boundary 
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Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, DavisDavisU.S.A.

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