TY - JOUR
T1 - The moduli of flat PGL(2, ℝ) connections on riemann surfaces
AU - Xia, Eugene Z.
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
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U2 - 10.1007/s002200050624
DO - 10.1007/s002200050624
M3 - Article
AN - SCOPUS:0033461753
SN - 0010-3616
VL - 203
SP - 531
EP - 549
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -