Phase space structure of Chern-Simons theory with a non-standard puncture

We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group G ? g* on a three-manifold of topology R × S_g,n⁸, where S_g,n⁸ is a surface of genus g with n + 1 punctures. At each puncture additional variables are introduced and coupled minimally to the Chern-Simons gauge field. The first n punctures are treated in the usual way and the additional variables lie on coadjoint orbits of G ? g *. The (n + 1)st puncture plays a distinguished role and the associated variables lie in the cotangent bundle of G ? g *. This allows us to impose a curvature singularity for the Chern-Simons gauge field at the distinguished puncture with an arbitrary Lie algebra valued coefficient. The treatment of the distinguished puncture is motivated by the desire to construct a simple model for an open universe in the Chern-Simons formulation of (2 + 1)-dimensional gravity. © 2006 Elsevier B.V. All rights reserved.