Skip to main content

The Gamma Element for Groups which Admit a Uniform Embedding into Hilbert Space

  • Conference paper
Recent Advances in Operator Theory, Operator Algebras, and their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 153))

Abstract

In {xc[17]}, it was shown that for every group Γ with a left-invariant metric d such that (Γ, d) has bounded geometry, and which admits a uniform embedding into Hilbert space, the Baum-Connes assembly map with coefficients is split injective. In this paper, we strengthen this result by showing that Γ has a gamma element.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Anatharaman-Delaroche, Amenability and Exactness for Dynamical Systems and their C*-Algebras. Preprint, Université d’Orléans, 2000.

    Google Scholar 

  2. P. Baum, A. Connes and N. Higson, Classifying Space for Proper Actions and K-theory of Group C*-Algebras. Contemporary Mathematics 167 (1994), 241–291.

    Google Scholar 

  3. J. Chabert and S. Echterhoff, Twisted Equivariant KK-Theory and the Baum-Connes Conjecture for Group Extensions. K-Theory 23 (2001), no. 2, 157–200.

    Google Scholar 

  4. J. Chabert, S. Echterhoff and R. Meyer, Deux remarques sur l’application de Baum-Connes. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 7, 607–610.

    Google Scholar 

  5. N. Higson, Bivariant K-Theory and the Novikov Conjecture. Geom. Funct. Anal. 10 (2000), no. 3, 563–581.

    Google Scholar 

  6. N. Higson and G. Kasparov, Operator K-Theory for Groups which Act Properly and Isometrically on Hilbert Space. Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 131–142 (electronic).

    Google Scholar 

  7. N. Higson and G. Kasparov, E-Theory and KK-Theory for Groups which Act Properly and Isometrically on Hilbert Space. Invent. Math. 144 (2001), no. 1, 23–74.

    Google Scholar 

  8. N. Higson and J. Roe, Amenable Group Actions and the Novikov Conjecture. J. Reine Angew. Math. 519 (2000), 143–153.

    Google Scholar 

  9. P. Julg, Travaux de N. Higson et G. Kasparov sur la conjecture de Baum-Connes. Séminaire Bourbaki. Vol. 1997/98, Astérisque 252 (1998), Exp. No. 841, 4, 151–183.

    Google Scholar 

  10. P. Julg, La conjecture de Baum-Connes à coefficients pour le groupe Sp(n,1). C. R. Math. Acad. Sci. Paris 334 (2002), no. 7, 533–538.

    Google Scholar 

  11. P. Julg and A. Valette, K-Theoretic Amenability for SL2(Qp), and the Action on the Associated Tree. J. Funct. Anal. 58 (1984), no. 2, 194–215.

    Google Scholar 

  12. G. Kasparov, Equivariant KK-Theory and the Novikov Conjecture. Inv. Math. 91 (1988), 147–201.

    Google Scholar 

  13. G. Kasparov and G. Skandalis, Groups Acting on Buildings, Operator K-Theory and Novikov’s Conjecture. K-Theory 4 (1991), 303–337.

    Article  Google Scholar 

  14. G. Kasparov and G. Skandalis, Groups Acting Properly on “Bolic” Spaces and the Novikov Conjecture. Preprint, 2000.

    Google Scholar 

  15. V. Lafforgue, K-théorie bivariante pour les algèbres de Banach et conjecture de Baum-Connes. Invent. Math. 149 (2002), no. 1, 1–95.

    Google Scholar 

  16. P.Y. Le Gall, Théorie de Kasparov équivariante et groupoïdes. I. K-Theory 16 (1999), no. 4, 361–390.

    Google Scholar 

  17. G. Skandalis, J.-L. Tu and G. Yu, Coarse Baum-Connes Conjecture and Groupoids. Preprint, 2000.

    Google Scholar 

  18. J.-L. Tu, La conjecture de Novikov pour les feuilletages hyperboliques. K-Theory 16, No. 2 (1999), 129–184.

    Google Scholar 

  19. J.-L. Tu, La conjecture de Novikov pour les feuilletages moyennables. K-Theory 17, No. 3 (1999), 215–264.

    Article  Google Scholar 

  20. J.-L. Tu, The Baum-Connes Conjecture and Discrete Group Actions on Trees. K-Theory 17 (1999), 303–318.

    Google Scholar 

  21. G. Yu, The Coarse Baum-Connes Conjecture for Spaces which Admit a Uniform Embedding into Hilbert Space. Invent. Math. 139 (2000), no. 1, 201–240.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Tu, JL. (2004). The Gamma Element for Groups which Admit a Uniform Embedding into Hilbert Space. In: Gaşpar, D., Timotin, D., Zsidó, L., Gohberg, I., Vasilescu, FH. (eds) Recent Advances in Operator Theory, Operator Algebras, and their Applications. Operator Theory: Advances and Applications, vol 153. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7314-8_18

Download citation

Publish with us

Policies and ethics