Word-hyperbolic surface bundles

Christopher Leininger (Illinois)

Monday 12th February, 2018 16:00-17:00 Maths 311B


Thurston's geometrization program revolutionized the study of 3-manifolds, and hyperbolic geometry became the primary tool in the study of these manifolds.  Soon after Gromov extracted the key features of hyperbolic geometry to study more general spaces---most importantly, finitely generated groups---and he has asked whether the analogue of the "hyperbolic part" of Thurston's geometrization holds for groups.  In this talk, I will describe a particular instance of Gromov's "hyperbolization question", motivated by Thurston's approach, and explain some partial results in this direction.  This is joint work with Bestvina, Bromberg, and Kent.

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