The moduli of flat PGL(2, ℝ) connections on riemann surfaces

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8 引文 斯高帕斯(Scopus)

摘要

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 w1([σ]) and w2([σ]). The set of representation classes with a fixed w1 ≠ 0 has two connected components. These two connected components are characterized by w2 being 0 or 1. For each fixed w1 ≠ 0, we prove that the component, characterized by w2 = 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 w2 = 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.

原文English
頁(從 - 到)531-549
頁數19
期刊Communications in Mathematical Physics
203
發行號3
DOIs
出版狀態Published - 1999

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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