TY - JOUR
T1 - The moduli of flat PU(p, p)-structures with large Toledo invariants
AU - Markman, E.
AU - Xia, Eugene Zhu
PY - 2002/5/1
Y1 - 2002/5/1
N2 - For a compact Riemann surface X of genus g > 1, Hom(π1 (X), PU(p, q))/PU(p, q) is the moduli space of flat PU(p, q)-connections on X. There are two invariants, the Chern class c and the Toledo invariant τ associated with each element in the moduli. The Toledo invariant is bounded in the range -2min(p, q)(g-1) ≤ τ ≤ 2min(p, q)(g - 1). This paper shows that the component, associated with a fixed τ > 2(max(p, q) - 1)(g - 1) (resp. τ < -2(max(p, q) - 1)(g - 1)) and a fixed Chern class c, is connected (The restriction on τ implies p = q).
AB - For a compact Riemann surface X of genus g > 1, Hom(π1 (X), PU(p, q))/PU(p, q) is the moduli space of flat PU(p, q)-connections on X. There are two invariants, the Chern class c and the Toledo invariant τ associated with each element in the moduli. The Toledo invariant is bounded in the range -2min(p, q)(g-1) ≤ τ ≤ 2min(p, q)(g - 1). This paper shows that the component, associated with a fixed τ > 2(max(p, q) - 1)(g - 1) (resp. τ < -2(max(p, q) - 1)(g - 1)) and a fixed Chern class c, is connected (The restriction on τ implies p = q).
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U2 - 10.1007/s002090100364
DO - 10.1007/s002090100364
M3 - Article
AN - SCOPUS:0036591074
SN - 0025-5874
VL - 240
SP - 95
EP - 109
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1
ER -