The equivalence of some residual properties of word-hyperbolic groups

By Ilya Kapovich, Daniel T. Wise. 2000

54 citations recorded by the source corpus.

Abstract We show that every word-hyperbolic group is residually finite if and only if every word-hyperbolic group has a finite quotient.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ef47ea1c5f7779136e867b42a648f67992366bf6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Vincent Guirardel
2. Gilbert Levitt
3. J. Manning
4. Daniel T. Wise
5. D. Groves
6. Mark F. Hagen
7. Franccois Dahmani
8. Radhika Gupta

In Geometry and Topology

1. Vincent Guirardel
2. Ian Agol
3. D. Groves
4. Gilbert Levitt
5. J. Manning
6. Daniel T. Wise
7. Denis V. Osin
8. Mark F. Hagen

In Mathematical Physics

1. Vincent Guirardel
2. Ian Agol
3. D. Groves
4. Gilbert Levitt
5. Daniel T. Wise
6. J. Manning
7. Denis V. Osin
8. Alessandro Sisto

Citations in the corpus

• Residual finiteness, QCERF, and fillings of hyperbolic groups (2008, background): “In the other direction, Kapovich and Wise show in [10] that if every hyperbolic group has a finite index subgroup, then every hyperbolic group is residually finite.”
• The outer space of a free product (2005, background): “It is not known whether there exist hyperbolic groups which are not virtually torsion-free (see [16]).”
• The residual finiteness of negatively curved polygons of finite groups (2002, background): “It is equivalent to the statement that every word-hyperbolic group has a proper finite index subgroup (see [ 18 ]), and to the statement that every word-hyperbolic group is virtually torsion-free (see [38, Proposition 6.2]).”