In the borderline dimension twice the rank, the marked Schottky space is simply connected with dense open part homotopy equivalent to a product of SO groups; a symmetric core deformation-retracts the space in all dimensions and the locus one dimension lower has two components.
Anosovflows,surfacegroupsandcurvesinprojectivespace
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A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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The topology of Schottky spaces in higher dimensions
In the borderline dimension twice the rank, the marked Schottky space is simply connected with dense open part homotopy equivalent to a product of SO groups; a symmetric core deformation-retracts the space in all dimensions and the locus one dimension lower has two components.
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Prescribing geodesics and a variational problem for Riemannian metrics
A variational functional E on Riemannian metrics vanishes precisely when geodesics realize prescribed unparametrised paths, and every conformal class on a surface admits a unique (up to homothety) conformally critical metric for E.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.