Maximal Sp(4,R) surface group representations, minimal immersions and cyclic surfaces

2015/03/11 by Collier, Brian
#Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1503.03526

Abstract

Let S be a closed surface of genus at least 2. For each maximal representation ρ: π₁(S)\rightarrowSp(4,ℝ) in one of the 2g-3 exceptional connected components, we prove there is a unique conformal structure on the surface in which the corresponding equivariant harmonic map to the symmetric space Sp(4,ℝ)/U(2) is a minimal immersion. Using a Higgs bundle parameterization of these components, we give a mapping class group invariant parameterization of such components as fiber bundles over Teichmüller space. Unlike Labourie's recent results on Hitchin components, these bundles are not vector bundles.

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