Communications in Mathematical Physics

, Volume 141, Issue 1, pp 211–223 | Cite as

2+1 gravity for genus >1

  • J. E. Nelson
  • T. Regge


In [1] we analysed the algebra of observables for the simple case of a genus 1 initial data surface ∑2 for 2+1 De Sitter gravity. Here we extend the analysis to higher genus. We construct for genus 2 the group of automorphismsH of the homotopy group π1 induced by the mapping class group. The groupH induces a groupD of canonical transformations on the algebra of observables which is related to the braid group for 6 threads.


Neural Network Statistical Physic Complex System Initial Data Nonlinear Dynamics 
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.
    Nelson, J.E., Regge, T.: Nucl. Phys. B328, 190 (1989)Google Scholar
  2. 2.
    Nelson, J.E., Regge, T., Zertuche, F.: Nucl. Phys. B339, 516 (1990)Google Scholar
  3. 3.
    Farkas, H.M., Kra, I.: Riemann surfaces. Berlin, Heidelberg, New York: Springer 1980Google Scholar
  4. 4.
    Majid, S.: Int. J. Mod. Phys. A5, 1 (1990)Google Scholar
  5. 5.
    Witten, E.: Nucl. Phys. B311, 46 (1989)Google Scholar
  6. 6.
    Birman, J.S.: Braids, links, and the mapping class group. Ann. Math. Stud. Princeton, NJ: Princeton University Press 1975Google Scholar
  7. 7.
    Carlip, S.: Time in 2+1 dimensional quantum gravity. Proc. Banff Conference on Gravitation, Canada 1990; and Moncrief, V.: J. Math. Phys.30, 12 (1989)Google Scholar
  8. 8.
    Nelson, J.E., Regge, T.: In preparationGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. E. Nelson
    • 1
  • T. Regge
    • 1
  1. 1.Dipartimento di Fisica Teorica dell'Università di TorinoTorinoItaly

Personalised recommendations