Inventiones mathematicae

, Volume 85, Issue 2, pp 263–302 | Cite as

Invariant functions on Lie groups and Hamiltonian flows of surface group representations

  • William M. Goldman


Group Representation Surface Group Invariant Function Hamiltonian Flow Surface Group Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abraham, R., Marsden, J.: Foundations of Mechanics. Second Edition. Reading, Massachusetts: Benjamin/Cummings 1978Google Scholar
  2. 2.
    Arnold, V.I.: Mathematical methods of classical mechanics. Graduate Texts in Mathematics 60, Berlin-Heidelberg-New York: Springer 1978Google Scholar
  3. 3.
    Brown, K.S.: Cohomology of groups. Graduate Texts in Mathematics 87. Berlin-Heidelberg-New York: Springer 1982Google Scholar
  4. 4.
    Cohen, J.M.: Poincaré 2-Complexes II. Chin. J. Math.6, 25–44 (1978)Google Scholar
  5. 5.
    Dold, A.: Lectures on Algebraic Topology, Berlin-Heidelberg-New York: Springer 1972Google Scholar
  6. 6.
    Goldman, W.: Discontinuous groups and the Euler class. Doctoral disseration. University of California 1980.Google Scholar
  7. 7.
    Goldman, W.: The symplectic nature of fundamental groups of surfaces. Adv. Math.54, 200–225 (1984)Google Scholar
  8. 8.
    Goldman, W.: Representations of fundamental groups of surfaces. Proceedings of Special Year in Topology, Maryland 1983–1984, Lect. Notes Math. (to appear)Google Scholar
  9. 9.
    Hass, J., Scott, G.P.: Intersections of curves on surfaces. Isr. J. Math.51, 90–120 (1985)Google Scholar
  10. 10.
    Helgason, S.: Differential geometry, Lie groups, and symmetric spaces. New York: Academic Press 1978Google Scholar
  11. 11.
    Hirsch, M.W.: Differential Topology, Graduate texts in mathematics 33, Berlin-Heidelberg-New York: Springer 1976Google Scholar
  12. 12.
    Johnson, D., Millson, J.: Deformation spaces of compact hyperbolic manifolds. In: Discrete groups in geometry and analysis. Proceedings of a Conference Held at Yale University in Honor of G.D. Mostow on his Sixtieth Birthday (to appear)Google Scholar
  13. 13.
    Kerckhoff, S.: The Nielsen realization problem. Ann. Math.117, 235–265 (1983)Google Scholar
  14. 14.
    Magnus, W.: The uses of 2 by 2 matrices in combinatorial group theory. A survey, Result. Math.4, 171–192 (1981)Google Scholar
  15. 15.
    Morgan, J.W., Shalen, P.B.: Valuations, trees, and degeneration of hyperbolic structures, I. Ann. Math.120, 401–476 (1984)Google Scholar
  16. 16.
    Steenrod, N.E.: The Topology of Fibre Bundles, Princeton NJ: Princeton University Press 1951Google Scholar
  17. 17.
    Weinstein, A.: Lectures on symplectic manifolds. C.B.M.S. 29, Am. Math. Soc., Providence R.I., 1977Google Scholar
  18. 18.
    Wolpert, S.: An elementary formula for the Fenchel-Nielsen twist. Comm. Math. Helv.56, 132–135 (1981)Google Scholar
  19. 19.
    Wolpert, S.: The Fenchel-Nielsen deformation. Ann. Math.115, 501–528 (1982)Google Scholar
  20. 20.
    Wolpert, S.: On the symplectic geometry of deformations of a hyperbolic surface. Ann. Math.117, 207–234 (1983)Google Scholar
  21. 21.
    Medina-Perea, A.: Groupes de Lie munis de pseudo-métriques de Riemann bi-invariantes. Séminaire de Géométrie Différentielle 1981–1982, Exposé 4, Institut de Mathématiques, Université des Sciences et Techniques du Languedoc, MontpellierGoogle Scholar
  22. 22.
    Papadopoulos, A.: Geometric intersection functions and Hamiltonian flows on the space of measured foliations on a surface. I.A.S. (preprint, 1984)Google Scholar
  23. 23.
    Procesi, C.: The invariant theory ofn×n matrices. Adv. Math.19, 306–381 (1976)Google Scholar
  24. 24.
    Weinstein, A.: The local structure of Poisson manifolds. J. Diff. Geom.18, 523–557 (1983)Google Scholar
  25. 25.
    Weinstein, A.: Poisson structures and Lie algebras, Proceedings of a conference on The Mathematical Heritage of Elie Cartan, Lyon, June 1984 (to appear in Asterisque)Google Scholar
  26. 26.
    Fathi, A.: The Poisson bracket on the space of measured foliations on a surface (preprint)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • William M. Goldman
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations