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From loom spaces to veering triangulations

https://doi.org/10.4171/GGD/742

Schleimer, Saul; Segerman, Henry (April 2024, Groups, Geometry, and Dynamics)

We introduce loom spaces, a generalisation of both the leaf spaces associated to pseudo- Anosov flows and the link spaces associated to veering triangulations. Following work of Guéritaud, we prove that there is a locally veering triangulation canonically associated to every loom space, and that the realisation of this triangulation is homeomorphic to R^3.
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Cohomology fractals, Cannon–Thurston maps, and the geodesic flow

https://doi.org/10.1080/10586458.2021.1994059

Bachman, David; Goerner, Matthias; Schleimer, Saul; Segerman, Henry (October 2022, Experimental Mathematics)

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Effective drilling and filling of tame hyperbolic 3-manifolds

https://doi.org/10.4171/CMH/536

Futer, David; Purcell, Jessica; Schleimer, Saul (January 2022, Commentarii Mathematici Helvetici)

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Effective bilipschitz bounds on drilling and filling

https://doi.org/10.2140/gt.2022.26.1077

Futer, David; Purcell, Jessica S; Schleimer, Saul (January 2022, Geometry & Topology)

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Essential loops in taut ideal triangulations

https://doi.org/10.2140/agt.2020.20.487

Schleimer, Saul; Segerman, Henry (January 2020, Algebraic & Geometric Topology)

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Cohomology Fractals

Bachman, David; Schleimer, Saul; Segerman, Henry (January 2020, Proceedings of Bridges 2020: Mathematics, Art, Music, Architecture, Education, Culture)
null (Ed.)
We introduce cohomology fractals; these are certain images associated to a cohomology class on a hyperbolic threemanifold. They include images made entirely from circles, and also images with no geometrically simple features. They are closely related to limit sets of kleinian groups, but have some key differences. As a consequence, we can zoom in almost any direction to arbitrary depth in real time. We present an implementation in the setting of ideal triangulations using ray-casting.
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