Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-25T08:57:37.754Z Has data issue: false hasContentIssue false

ON KLEINIAN GROUPS WITH THE SAME SET OF AXES

Published online by Cambridge University Press:  01 December 2008

BAOHUA XIE
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, People’s Republic of China (email: [email protected])
YUEPING JIANG
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha, 410082, People’s Republic of China (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

J. W. Anderson (1996) asked whether two finitely generated Kleinian groups with the same set of axes are commensurable. We give some partial solutions.

Type
Research Article
Copyright
Copyright © 2009 Australian Mathematical Society

References

[1]Anderson, J. W., ‘The limit set intersection theorem for finitely generated Kleinian groups’, Math. Res. Lett. 3 (1996), 675692.CrossRefGoogle Scholar
[2]Bass, H. and Morgan, J., The Smith Conjecture (Academic Press, New York, 1984).Google Scholar
[3]Beardon, A. F., The Geometry of Discrete Goups (Springer, New York, 1983).CrossRefGoogle Scholar
[4]Bestvina, M., Questions in geometric group theory, 2004,http://www.math.utah.edu/∼bestvina/eprints/questions-updated.pdf.Google Scholar
[5]Hempel, J., ‘The finitely generated intersection property for Kleinian groups’, in: Knot Theory and Manifolds, Lectures Notes in Mathematics, 1144 (Springer, Berlin, 1985), pp. 1824.CrossRefGoogle Scholar
[6]Long, D. D. and Reid, A. W., ‘On Fuchsian groups with the same set of axes’, Bull. London Math. Soc. 30 (1998), 533538.CrossRefGoogle Scholar
[7]Mess, G., ‘Fuchsian groups with the same simple axes’, Preprint, 1990.Google Scholar
[8]Ratcliffe, J. G., Foundations of Hyperbolic Manifolds (Springer, New York, 1994).CrossRefGoogle Scholar
[9]Susskind, P., ‘An infinitely generated intersection of the hyperbolic group’, Proc. Amer. Math. Soc. 129 (2001), 26432646.CrossRefGoogle Scholar
[10]Susskind, P. and Swarup, G., ‘Limit sets of geometrically finite hyperbolic groups’, Amer. J. Math. 114 (1992), 233250.CrossRefGoogle Scholar