### Abstract

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,n}^{8}, where S_{g,n}^{8} 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.

Original language | English |
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Pages (from-to) | 425-456 |

Number of pages | 32 |

Journal | Nuclear Physics B |

Volume | 738 |

Issue number | 3 |

DOIs | |

Publication status | Published - 27 Mar 2006 |

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## Cite this

*Nuclear Physics B*,

*738*(3), 425-456. https://doi.org/10.1016/j.nuclphysb.2006.01.014