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

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)531-549
Number of pages19
JournalCommunications in Mathematical Physics
Volume203
Issue number3
DOIs
Publication statusPublished - 1999 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'The moduli of flat PGL(2, ℝ) connections on riemann surfaces'. Together they form a unique fingerprint.

Cite this