Intersecting limit sets of Kleinian subgroups and Susskind’s question
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- by Tushar Das and David Simmons PDF
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Abstract:
We construct a non-elementary Fuchsian group that admits two non-elementary subgroups with trivial intersection and whose radial limit sets intersect non-trivially. This negatively answers a question of Perry Susskind [J. Analyse Math. 52 (1989), pp. 26–38] that was stated as a conjecture by James W. Anderson [Comput. Methods Funct. Theory 14 (2014), no. 2-3, pp. 453–464].References
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Additional Information
- Tushar Das
- Affiliation: Department of Mathematics & Statistics, University of Wisconsin–La Crosse, 1725 State Street, La Crosse, Wisconsin 54601
- MR Author ID: 958150
- ORCID: 0000-0002-3158-4972
- Email: tdas@uwlax.edu
- David Simmons
- Affiliation: Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom
- MR Author ID: 1005497
- Email: David.Simmons@york.ac.uk
- Received by editor(s): March 17, 2018
- Received by editor(s) in revised form: June 7, 2018
- Published electronically: April 29, 2020
- Additional Notes: The first-named author was supported in part by a 2017–2018 Faculty Research Grant from the University of Wisconsin–La Crosse.
The second-named author was supported by the EPSRC Programme Grant EP/J018260/1. - Communicated by: Nimish Shah
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 3203-3207
- MSC (2010): Primary 20H10, 30F40, 22E40
- DOI: https://doi.org/10.1090/proc/14357
- MathSciNet review: 4108830