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Communications in Mathematical Physics

, Volume 203, Issue 3, pp 531–549 | Cite as

The Moduli of Flat PGL(2,ℝ) Connections on¶Riemann Surfaces

  • Eugene Z. Xia

Abstract:

Suppose X is a compact Riemann surface with genus g>1. Each class [σ] ∈ Hom(π1(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.

Keywords

Vector Bundle Riemann Surface Representation Class Total Space Compact Riemann Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Eugene Z. Xia
    • 1
  1. 1.Department of Mathematics,University of Arizona, Tucson, AZ 85721, USA. E-mail: exia@math.arizona.eduUS

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