Skip to main content
Log in

RAAGs in Ham

  • Published:
Geometric and Functional Analysis Aims and scope Submit manuscript

Abstract

We prove that every RAAG (Right Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of every symplectic manifold.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. Bergeron, F. Haglund, and D. Wise. A combination theorem for special cube complexes, Preprint.

  2. Casson A., Bleiler S.: Automorphisms of Surfaces After Nielsen and Thurston, London Mathematical Society Student Texts, 9. Cambridge University Press, Cambridge (1988)

    Book  Google Scholar 

  3. M. Clay, C. Leininger, and J. Mangahas. The geometry of right angled Artin subgroups of mapping class groups. arXiv:1007.1129, 2010.

  4. Charney R.: An introduction to right-angled Artin groups. Geometriae Dedicata 125, 141–158 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Crisp J., Wiest B.: Quasi-isometrically embedded subgroups of braid and diffeomorphism groups. Transactions of American Mathematics Society 359, 5485–5503 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Farb and D. Margalit A Primer on Mapping Class Groups. Princeton University Press (2011).

  7. Franks J., Handel M.: Distortion elements in group actions on surfaces. Duke Mathematics Journal 131, 441–468 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Fisher. Groups acting on Manifolds: Around the Zimmer program. In: Geometry, rigidity, and group actions, Chicago Lectures in Mathematics University Chicago Press, Chicago, IL (2011), pp. 72–157.

  9. L. Funar. On power subgroups of mapping class groups. arXiv:0910.1493, 2009.

  10. Greene R., Shiohama K.: Diffeomorphisms and volume-preserving embeddings of noncompact manifolds. Transactions of the American Mathematics Society 255, 403–414 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Hermiller and J. Meier. Algorithms and geometry for graph products of groups. Journal of Algebra, 171 (1995), no. 1, 230–257.

    Google Scholar 

  12. Hlineny P.: 20 years of Negami’s planar cover conjecture. Graphs and Combinatorics 26, 525–536 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. N. Ivanov. Mapping class groups. In: Handbook of Geometric Topology, North-Holland, Amsterdam (2002), pp. 523–633.

  14. S. Kim and T. Koberda. Embeddability between right-angled Artin groups. arXiv:1007.1118, 2010.

  15. T. Koberda. Right-angled Artin groups and a generalized isomorphism problem for finitely generated subgroups of mapping class groups. arXiv:1007.1118, 2010.

  16. L. Polterovich. Growth of maps, distortion in groups and symplectic geometry. Invented Mathematics, 150 (2002), no. 3, pp. 655–686.

  17. J. Ratcliffe Foundations of Hyperbolic Manifolds. Springer Verlag, (1994).

  18. Rieck Y., Yamashita Y.: Finite planar emulators for K 4,5—4K 2 and K 1,2,2,2 and Fellows+ Conjecture. European Journal of Combinatorics 31, 903–907 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Kapovich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kapovich, M. RAAGs in Ham. Geom. Funct. Anal. 22, 733–755 (2012). https://doi.org/10.1007/s00039-012-0180-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00039-012-0180-9

Keywords

Navigation