The Moduli of Flat PU(p,p)-Structures with Large Toledo Invariants

الأصل · EN

For a compact Riemann surface X of genus g > 1, (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).