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Intersecting limit sets of Kleinian subgroups and Susskind's question


Authors: Tushar Das and David Simmons
Journal: Proc. Amer. Math. Soc. 148 (2020), 3203-3207
MSC (2010): Primary 20H10, 30F40, 22E40
DOI: https://doi.org/10.1090/proc/14357
Published electronically: April 29, 2020
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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].


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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
Email: tdas@uwlax.edu

David Simmons
Affiliation: Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom
Email: David.Simmons@york.ac.uk

DOI: https://doi.org/10.1090/proc/14357
Keywords: Fuchsian group, Kleinian group, Schottky group, limit set, hyperbolic space
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
Article copyright: © Copyright 2020 American Mathematical Society