## Abstract

Suppose X is a compact Riemann surface with genus g > 1. Each class [σ] ∈ Hom(π_{1}(X), PGL(2, ℝ))/PGL(2, ℝ) is associated with the first and second Stiefel-Whitney classes w_{1}([σ]) and w_{2}([σ]). The set of representation classes with a fixed w_{1} ≠ 0 has two connected components. These two connected components are characterized by w_{2} being 0 or 1. For each fixed w_{1} ≠ 0, we prove that the component, characterized by w_{2} = 0, contains an open dense set diffeomorphic to the total space of a vector bundle of rank 2g - 2 over a once punctured algebraic torus of dimension g - 1. The other component, characterized by w_{2} = 1, contains an open dense set diffeomorphic to the total space of a vector bundle of rank 2g - 2 over an algebraic torus of dimension g - 1.

Original language | English |
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Pages (from-to) | 531-549 |

Number of pages | 19 |

Journal | Communications in Mathematical Physics |

Volume | 203 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1999 Jan 1 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics