Toledo Invariants of 2-Orbifolds and Higgs Bundles on Elliptic Surfaces

摘要

In this paper we investigate the space of conjugacy classes of semisimple representations ρ: π_1~(orb)(O) → U(2,1) for 2-orbifolds arising as the base of a Seifert fibration. To each connected component in the corresponding representation variety, we associate a number called the orbifold Toledo invariant. Our main result (Theorem 6.2) explicitly computes all values that the orbifold Toledo invariant takes on when the Seifert manifold Y is a homology 3-sphere.