TY - JOUR
T1 - The Moduli of Flat U(p, 1) Structures on Riemann Surfaces
AU - Xia, Eugene Zhu
PY - 2003/3/1
Y1 - 2003/3/1
N2 - For X a smooth projective curve over C of genus g > 1, Hom +(π1(X), U(p, 1))/ U(p, 1) is the moduli space of flat semi-simple U(p, 1)-connections on X. There is an integer invariant, τ, the Toledo invariant associated with each element in Hom+(π 1(X), U(p, 1))/ U(p, 1). This paper shows that Hom +(π1(X), U(p, 1))/U(p, 1) has one connected component corresponding to each τ ε 2ℤ with -2(g - 1) ≤ τ ≤ 2(g - 1). Therefore the total number of connected components is 2(g - 1) + 1.
AB - For X a smooth projective curve over C of genus g > 1, Hom +(π1(X), U(p, 1))/ U(p, 1) is the moduli space of flat semi-simple U(p, 1)-connections on X. There is an integer invariant, τ, the Toledo invariant associated with each element in Hom+(π 1(X), U(p, 1))/ U(p, 1). This paper shows that Hom +(π1(X), U(p, 1))/U(p, 1) has one connected component corresponding to each τ ε 2ℤ with -2(g - 1) ≤ τ ≤ 2(g - 1). Therefore the total number of connected components is 2(g - 1) + 1.
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U2 - 10.1023/A:1023675007667
DO - 10.1023/A:1023675007667
M3 - Article
AN - SCOPUS:0038403600
SN - 0046-5755
VL - 97
SP - 33
EP - 43
JO - Geometriae Dedicata
JF - Geometriae Dedicata
IS - 1
ER -