Extension of geodesic algebras to continuous genus
  Using the Penner--Fock parameterization for Teichmuller spaces of Riemann surfaces with holes, we construct the string-like free-field representation of the Poisson and quantum algebras of geodesic functions in the continuous-genus limit. The mapping class group acts naturally in the obtained representation. 
L. Chekhov (Steklov Mathematical Institute and Institute for   Experimental and Theoretical Physics, Moscow, Russia), J.E.Ne...