The Moduli of Flat U(p, 1) Structures on Riemann Surfaces

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Abstract

For X a smooth projective curve over C of genus g > 1, Hom +1(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+1(X), U(p, 1))/ U(p, 1). This paper shows that Hom +1(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.

Original languageEnglish
Pages (from-to)33-43
Number of pages11
JournalGeometriae Dedicata
Volume97
Issue number1
DOIs
Publication statusPublished - 2003 Mar 1

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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