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Award ID contains: 2002187

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  1. ; (, Journal of Topology)
    Abstract We introduce and motivate the definition of the virtual Rokhlin property for topological groups. We then classify the 2‐manifolds whose homeomorphism groups have the virtual Rokhlin property. We also establish the analogous result for mapping class groups of 2‐manifolds. 
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  2. ; (, Geometriae Dedicata)
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  3. ; (, Groups, Geometry, and Dynamics)
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  4. ; (, Mathematische Zeitschrift)
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  5. ; (, Glasnik Matematicki)
    In this note we make progress toward a conjecture of Durham–Fanoni–Vlamis, showing that every infinite-type surface with fi­ni­te-invariance index \(1\) and no nondisplaceable compact subsurfaces fails to have a good graph of curves, that is, a connected graph where vertices represent homotopy classes of essential simple closed curves and with a natural mapping class group action having infinite diameter orbits. Our arguments use tools developed by Mann–Rafi in their study of the coarse geometry of big mapping class groups. 
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