THE ACTION OF THE MAPPING CLASS GROUP ON MAXIMAL REPRESENTATIONS

THE ACTION OF THE MAPPING CLASS GROUP ON MAXIMAL REPRESENTATIONS

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by Anna Wienhard

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@MISC{Wienhard_theaction,
    author = {Anna Wienhard},
    title = {THE ACTION OF THE MAPPING CLASS GROUP ON MAXIMAL REPRESENTATIONS},
    year = {}
}

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Abstract

Abstract. Let Γg be the fundamental group of a closed oriented Riemann surface Σg, g ≥ 2, and let G be a simple Lie group of Hermitian type. The Toledo invariant defines the subset of maximal representations Repmax(Γg, G) in the representation variety Rep(Γg, G). Repmax(Γg, G) is a union of connected components with similar properties as Teichmüller space T (Σg) = Repmax(Γg, PSL(2, R)). We prove that the mapping class group ModΣg acts properly on Repmax(Γg, G) when G = Sp(2n, R), SU(n, n), SO ∗ (4n), Spin(2, n).

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