University of Birmingham > Talks@bham > Algebra Seminar > Classical and non-classical subgroups of Schottky groups

Classical and non-classical subgroups of Schottky groups

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If you have a question about this talk, please contact David Craven.

Schottky groups are among the earliest examples given of Kleinian groups acting on hyperbolic 3-space. The proof by Marden of the existence of nonclassical Schottky groups, and the subsequent construction of explicit examples in rank 2 by Yamamoto, led to the question of whether every Riemann surface can be uniformed by a classical Schottky group. Consideration of this difficult question quickly leads to the conclusion that in order to make any significant progress, we need to have some clear understanding of the differences between classical and non-classical Schottky groups. The purpose of this talk is to define what we mean by classical and non-classical Schottky groups and to present results describing the possibilities for classical or non-classical subgroups in both classical and non-classical Schottky groups.

This talk is part of the Algebra Seminar series.

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