We prove that (topologically) rigid actions of surface groups on the circle by homeomorphisms are necessarily geometric, namely, they are semiconjugate to an embedding as a cocompact lattice in a Lie group acting transitively on S1. This gives the converse to a theorem of the first author; thus characterizing geometric actions as the unique isolated points in the “character space” of surface group actions on S1.
CITATION STYLE
Mann, K., & Wolff, M. (2024). Rigidity and geometricity for surface group actions on the circle. Geometry and Topology, 28(5), 2345–2398. https://doi.org/10.2140/gt.2024.28.2345
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