Maximal Surface Group Representations in Isometry Groups of Classical Hermitian Symmetric Spaces
نویسندگان
چکیده
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.
منابع مشابه
Surface Group Representations with Maximal Toledo Invariant
We develop the theory of maximal representations of the fundamental group π1(Σ) of a compact connected oriented surface Σ with boundary ∂Σ, into the isometry group of a Hermitian symmetric space X or, more generally, a group of Hermitian type G. For any homomorphism ρ : π1(Σ) → G, we define the Toledo invariant T(Σ, ρ), a numerical invariant which is in general not a characteristic number, but ...
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تاریخ انتشار 2005