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Cores for quasiconvex actions


Authors: Michah Sageev and Daniel T. Wise
Journal: Proc. Amer. Math. Soc. 143 (2015), 2731-2741
MSC (2010): Primary 20F67
DOI: https://doi.org/10.1090/S0002-9939-2015-12297-6
Published electronically: February 26, 2015
MathSciNet review: 3336599
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Abstract: We prove that any full relatively quasiconvex subgroup of a relatively hyperbolic group acting on a CAT(0) cube complex has a convex cocompact core. We give an application towards separability of quasiconvex subgroups of the fundamental group of a special cube complex.


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Additional Information

Michah Sageev
Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
Email: sageevm@techunix.technion.ac.il

Daniel T. Wise
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada H3A 0B9
Email: wise@math.mcgill.ca

DOI: https://doi.org/10.1090/S0002-9939-2015-12297-6
Received by editor(s): March 13, 2012
Received by editor(s) in revised form: August 7, 2012, and April 15, 2013
Published electronically: February 26, 2015
Additional Notes: The first author’s research was supported by ISF grant #530/11
The second author’s research was supported by NSERC
Communicated by: Kevin Whyte
Article copyright: © Copyright 2015 American Mathematical Society