Fuchsian groups , coverings of Riemann surfaces , subgroup growth , random quotients and random walks

@inproceedings{Liebeck2003FuchsianG,
  title={Fuchsian groups , coverings of Riemann surfaces , subgroup growth , random quotients and random walks},
  author={Martin W. Liebeck},
  year={2003}
}
Fuchsian groups (acting as isometries of the hyperbolic plane) occur naturally in geometry, combinatorial group theory, and other contexts. We use character-theoretic and probabilistic methods to study the spaces of homomorphisms from Fuchsian groups to symmetric groups. We obtain a wide variety of applications, ranging from counting branched coverings of Riemann surfaces, to subgroup growth and random finite quotients of Fuchsian groups, as well as random walks on symmetric groups. In… CONTINUE READING
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