Skip to main content



We give a means of estimating the equivariant compression of a group G in terms of properties of open subgroups G i G whose direct limit is G. Quantifying a result by Gal, we also study the behaviour of the equivariant compression under amalgamated free products G 1∗H G 2 where H is of finite index in both G 1 and G 2.

Hide All
1. Antolin, Y. and Dreesen, D., The Haagerup property is stable under graph products, preprint, 2013.
2. Arzhantseva, G. N., Guba, V. S. and Sapir, M. V., Metrics on diagram groups and uniform embeddings in a Hilbert space, Comment. Math. Helv. 81 (4) (2006), 911929.
3. Arzhantseva, G., Druţu, C. and Sapir, M., Compression functions of uniform embeddings of groups into Hilbert and Banach spaces, J. Reine Angew. Math. 633 (2009), 213235.
4. Austin, T., Amenable groups with very poor compression into Lebesgue spaces, Duke Math. J. 159 (2) (2011), 187222.
5. Austin, T., Naor, A. and Peres, Y., The wreath product of $\mathbb{Z}$ with $\mathbb{Z}$ has Hilbert compression exponent $\frac{2}{3}$ , Proc. Amer. Math. Soc. 137 (1) (2009), 8590.
6. Bekka, B., de la Harpe, P. and Valette, A., Kazhdan's property (T), New Mathematical Monographs, vol. 11 (Cambridge University Press, Cambridge, 2008).
7. Cherix, P.-A., Cowling, M., Jolissaint, P., Julg, P. and Valette, A., Groups with the Haagerup property, Progress in Mathematics, vol. 197 (Birkhäuser Verlag, Basel, 2001), Gromov's a-T-menability.
8. Cornulier, Y., Stalder, Y. and Valette, A., Proper actions of wreath products and generalizations, Trans. Amer. Math. Soc. 364 (6) (2012), 31593184.
9. de Cornulier, Y., R. Tessera and A. Valette, Isometric group actions on Hilbert spaces: Growth of cocycles, Geom. Funct. Anal. 17 (3) (2007), 770792.
10. de la Harpe, P. and Valette, A., La propriété (T) de Kazhdan pour les groupes localement compacts (avec un appendice de Marc Burger), Number 175. 1989, With an appendix by M. Burger.
11. Dreesen, D., Hilbert space compression for free products and HNN-extensions, J. Funct. Anal. 261 (12) (2011), 35853611.
12. Gal, Ś. R., a-T-menability of groups acting on trees, Bull. Austral. Math. Soc. 69 (2) (2004), 297303.
13. Guentner, E. and Kaminker, J., Exactness and the Novikov conjecture, Topology 41 (2) (2002), 411418.
14. Guentner, E. and Kaminker, J., Exactness and uniform embeddability of discrete groups, J. London Math. Soc. 70 (3) (2004), 703718.
15. Hewitt, E. and Ross, K. A., Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152 (Springer-Verlag, New York, 1970).
16. Lafforgue, V., Un renforcement de la propriété (T), Duke Math. J. 143 (3) (2008), 559602.
17. Li, S., Compression bounds for wreath products, Proc. Amer. Math. Soc. 138 (8) (2010), 27012714.
18. Naor, A. and Peres, Y., Embeddings of discrete groups and the speed of random walks, Int. Math. Res. Not. (2008). doi: 10.1093/imrn/rnn076.
19. Stalder, Y. and Valette, A., Wreath products with the integers, proper actions and Hilbert space compression, Geom. Dedicata 124 (2007), 199211.
20. Tessera, R., Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces, Comment. Math. Helv. 86 (3) (2011), 499535.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 32 *
Loading metrics...

Abstract views

Total abstract views: 143 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th March 2018. This data will be updated every 24 hours.