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Relative cubulations and groups with a 2-sphere boundary

Published online by Cambridge University Press:  24 March 2020

Eduard Einstein
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL60607-7045, USA email [email protected]
Daniel Groves
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL60607-7045, USA email [email protected]

Abstract

We introduce a new kind of action of a relatively hyperbolic group on a $\text{CAT}(0)$ cube complex, called a relatively geometric action. We provide an application to characterize finite-volume Kleinian groups in terms of actions on cube complexes, analogous to the results of Markovic and Haïssinsky in the closed case.

MSC classification

Type
Research Article
Copyright
© The Authors 2020

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Footnotes

The second author was partially supported by the National Science Foundation, DMS-1507067.

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