THE MODULI OF FLAT U(p, 1) STRUCTURES ON RIEMANN SURFACES
نویسنده
چکیده
For a compact Riemann surface X of genus g > 1, Hom(π1(X),U(p, 1))/U(p, 1) is the moduli space of flat U(p, 1)connections on X . There is an integer invariant, τ , the Toledo invariant associated with each element in Hom(π1(X),U(p, 1))/U(p, 1). If q = 1, then −2(g − 1) ≤ τ ≤ 2(g − 1). This paper shows that Hom(π1(X),U(p, 1))/U(p, 1) has one connected component corresponding to each τ ∈ 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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تاریخ انتشار 2008