On the real spectrum compactification of character varieties

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• Marc Burger (ETH Zürich)
• Wednesday 09 July 2025, 09:15-10:15
• Seminar Room 1, Newton Institute.

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NPCW06 - Non-positive curvature and applications

In this talk I will describe various aspects of our work on the real spectrum compactification of the G-character variety X(F,G) of a finitely generated group F. This compactification is mindful of the algebraic topology of X(F,G) and contains a lot of information: for instance, points in its boundary lead canonically to F-actions on lambda buildings; these objects generalize lambda trees and affine Bruhat-Tits buildings.   When F is a compact surface group and G admits a theta positive structure, X(F,G) has connected components consisting entirely of faithful representations with discrete image, these components are the higher Teichmueller spaces. For such a component T, the mapping class group Out(F) acts with virtually abelian stabilizers on the real spectrum compactification Rspec(T) of T. This is based on a relation between Rspec(T) and the compactification of T by geodesic currents. I will explain how this relation leads to a new proof of a recent result of Charlie Reid establishing restrictions on boundary currents when G= PSL and T is the Hitchin component. Joint work with A.Iozzi, A.Parreau, B.Pozzetti

This talk is part of the Isaac Newton Institute Seminar Series series.

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