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The real spectrum compactification of character varieties

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arxiv 2311.01892 v2 pith:PSTCFBNY submitted 2023-11-03 math.GR math.AGmath.DGmath.GT

Marc Burger , Alessandra Iozzi , Anne Parreau , Maria Beatrice Pozzetti This is my paper · ORCID
classification math.GRmath.AGmath.DGmath.GT
keywords compactificationbuilding-likecharactergroupsrealspacesspectrumvarieties
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We study the real spectrum compactification of character varieties of finitely generated groups in semisimple Lie groups. This provides a compactification with good topological properties, and we interpret the boundary points in terms of actions on building-like spaces. Among the applications we give a general framework guaranteeing the existence of equivariant harmonic maps in building-like spaces.

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  1. Holonomy Asymptotics along Quartic Differential Rays

    math.DG 2026-08 accept novelty 6.0 of 10

    The leading exponential growth rates of all singular values and eigenvalue moduli of PSp(4,R) Hitchin holonomies along quartic rays are explicit integrals of fourth roots of the quartic differential over saddle connections.

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