Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-25T06:08:04.133Z Has data issue: false hasContentIssue false
  • English
  • Français

The A-T-menability of some graphs of groups with cyclic edge groups

Published online by Cambridge University Press:  19 September 2016

MATHIEU CARETTE ,
DANIEL T. WISE  and
DANIEL J. WOODHOUSE
MATHIEU CARETTE
Affiliation:
Dept. of Math. & Stats. McGill University Montreal, QC, CanadaH3A 0B9. e-mails: mathieu.carette@gmail.com; wise@math.mcgill.ca; daniel.woodhouse@mail.mcgill.ca
DANIEL T. WISE
Affiliation:
Dept. of Math. & Stats. McGill University Montreal, QC, CanadaH3A 0B9. e-mails: mathieu.carette@gmail.com; wise@math.mcgill.ca; daniel.woodhouse@mail.mcgill.ca
DANIEL J. WOODHOUSE
Affiliation:
Dept. of Math. & Stats. McGill University Montreal, QC, CanadaH3A 0B9. e-mails: mathieu.carette@gmail.com; wise@math.mcgill.ca; daniel.woodhouse@mail.mcgill.ca
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that certain graphs of groups with cyclic edge groups are aTmenable. In particular, this holds when each vertex group is either virtually special or acts properly and semisimply on ℍn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 1 , July 2017 , pp. 145 - 159
Copyright
Copyright © Cambridge Philosophical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[Car14] Carette, M. The haagerup property is not invariant under quasi-isometry. With an appendix by Sylvain Arnt, Thibault Pillon, Alain Valette. Preprint, http://arxiv.org/abs/1403.5446, 2014.Google Scholar
[CCJ+01] Cherix, P.-A., Cowling, M., Jolissaint, P., Julg, P. and Valette, A. Groups with the Haagerup property. Progr. Math., vol. 197 (Birkhäuser Verlag, Basel, 2001). Gromov's a-T-menability.Google Scholar
[CDH10] Chatterji, I., Druţu, C. and Haglund, F. Kazhdan and Haagerup properties from the median viewpoint. Adv. Math. 225 (2) (2010), 882–921.Google Scholar
[CMV04] Cherix, P.-A., Martin, F. and Valette, A. Spaces with measured walls, the Haagerup property and property (T). Ergodic Theory Dynam. Systems 24 (6) (2004), 1895–1908.Google Scholar
[dlR93] de la Rue, T. Espaces de Lebesgue. In Séminaire de Probabilités, XXVII. Lecture Notes in Math., vol. 1557 (Springer, Berlin, 1993), 15–21.Google Scholar
[Gro93] Gromov, M. Asymptotic invariants of infinite groups. In Geometric Group Theory 2 (Sussex, 1991) (Cambridge University Press, Cambridge, 1993), 1–295.Google Scholar
[Hag06] Haglund, F. Commensurability and separability of quasiconvex subgroups. Algebr. Geom. Topol. 6 (electronic), (2006), 949–1024.Google Scholar
[HW08] Haglund, F. and Wise, D. T. Special cube complexes. Geom. Funct. Anal. 17 (5) (2008), 1551–1620.Google Scholar
[Jol00] Jolissaint, P. Borel cocycles, approximation properties and relative property T. Ergodic Theory Dynam. Systems 20 (2) (2000), 483–499.Google Scholar
[Rob98] Robertson, G. Crofton formulae and geodesic distance in hyperbolic spaces. J. Lie Theory. 8 (1) (1998), 163–172.Google Scholar
[SW15] Sageev, M. and Wise, D. T. Cores for quasiconvex actions. Proc. Amer. Math. Soc. 143 (7) (2015), 2731–2741.Google Scholar
[WW15] Wise, D. T. and Woodhouse, D. J. A cubical flat torus theorem and the bounded packing property. Israel J. Math. (To appear), 1–19.Google Scholar