## Abstract

We show how to construct a topological quantum field theory which corresponds to a given moduli space. We apply this method to the case of flat gauge connections defined over a Riemann surface and discuss its relations with the Chern-Simons theory and conformal field theory. Geometrical properties are invoked to prove that the observables of those theories are not trivial. The case of the SO(2,1) group is separately discussed. A topological field theory is linked to the moduli space of "self-dual" connections over Riemann surfaces. Another relation between the Chern-Simons theory and topological quantum field theory in three dimensions is established. We present the theory which corresponds to three-dimensional gravity. Expressions for the Casson invariants are given. Possible generalizations are briefly discussed.

Original language | English |
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Pages (from-to) | 2080-2094 |

Number of pages | 15 |

Journal | Physical Review D |

Volume | 42 |

Issue number | 6 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |