Toledo invariants of Higgs bundles on elliptic surfaces associated to base orbifolds of Seifert fibered homology 3-spheres

Details Toledo invariants of Higgs bundles on elliptic surfaces associated to base orbifolds of Seifert fibered homology 3-spheres Toledo invariants of Higgs bundles on elliptic surfaces associated to base orbifolds of Seifert fibered homology 3-spheres

2005-03-23

arxiv.org/abs/math/0503509v2

Mathematics

Geometric Topology

39 pages; replacement contains alternate proofs of verticality

Scientific paper

To each connected component in the space of semisimple representations from the orbifold fundamental group of the base orbifold of a Seifert fibered homology 3-sphere into the Lie group U(2,1), we associate a real number called the "orbifold Toledo invariant." For each such orbifold, there exists an elliptic surface over it, called a Dolgachev surface. Using the theory of Higgs bundles on these Dolgachev surfaces, we explicitly compute all values taken on by the orbifold Toledo invariant.

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