A Jørgensen–Thurston theorem for homomorphisms

We provide a description of the structure of the set of homomorphisms from a finitely generated group to any torsion-free ( $3$ –dimensional) Kleinian group with uniformly bounded finite covolume. This is analogous to the Jørgensen–Thurston Theorem in hyperbolic geometry.

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Keywords

hyperbolic geometry, limit group, Dehn extension

Mathematical Subject Classification 2010

Primary: 57M07

Secondary: 57M50, 20F65

References

Publication

Received: 27 December 2011

Revised: 22 March 2012

Accepted: 4 April 2012

Published: 11 June 2012

Authors

Yi Liu
Department of Mathematics University of California at Berkeley 970 Evans Hall Berkeley CA 94720-3840 USA
http://math.berkeley.edu/~yliu

Volume 12, issue 3 (2012)

Yi Liu

Abstract