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Viewing the Thurston geometries from the inside

Banff International Research Station for Mathematical Innovation and Discovery

Thurston's geometrization conjecture, proved by Perelman in 2003, states that every three-dimensional manifold can be cut into a collection of pieces, each of which has one of eight geometries. These "Thurston geometries" include the euclidean, spherical, and hyperbolic geometries, the products of the two-dimensional spherical and hyperbolic geometries with the euclidean line, and three other, stranger geometries. In this talk, I'll describe joint work with Rémi Coulon, Sabetta Matsumoto, and Steve Trettel, in which we simulate the "inside view" from within each of the Thurston geometries. That is we generate images assuming that light travels along geodesics in the geometry of the manifold. Many of our animations and interactive web-apps are available on our website http://www.3-dimensional.space/

Mathematics; Geometry; Education; Art; Research

video/mp4

Author affiliation: Oklahoma State University

2021-08-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/79366

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/