Published by De Gruyter July 6, 2017

Full box spaces of free groups

Thiebout Delabie

From the journal Journal of Group Theory

https://doi.org/10.1515/jgth-2017-0022

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Abstract

In this paper we investigate full box spaces and coarse equivalences between them. We do this in two parts. In part one we compare the full box spaces of free groups on different numbers of generators. In particular, the full box space of a free group Fk is not coarsely equivalent to the full box space of a free group Fd, if d≥8⁢k+10. In part two we compare □f⁢ℤn to the full box spaces of 2-generated groups. In particular, we prove that the full box space of ℤn is not coarsely equivalent to the full box space of any 2-generated group, if n≥3.

Communicated by Pierre-Emmanuel Caprace

Funding source: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Award Identifier / Grant number: 200021_163417

Funding statement: Supported by grant 200021_163417 of the Swiss National Science Foundation.

Acknowledgements

The author would like to thank Ana Khukhro and Alain Valette for the many useful comments.

References

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[3] A. Lubotzky and D. Segal, Subgroup Growth, Progr. Math. 212, Birkhäuser, Basel, 2012. Search in Google Scholar

Received: 2016-8-16

Revised: 2017-5-30

Published Online: 2017-7-6

Published in Print: 2018-1-1

Full box spaces of free groups

Abstract

Acknowledgements

References

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