Hyperbolicity of certain one-relator groups

Abstract: The primitivity rank of an element \(w\) of a free group \(F\) is defined as the minimal rank of a subgroup containing w as an imprimitive element. Recent work of Louder and Wilton has shown that there is a strong connection between this quantity and the subgroup structure of the one-relator group \(F/\langle \langle w \rangle \rangle\). In particular, they show that one-relator groups whose defining relation has primitivity rank at least three cannot contain Baumslag—Solitar subgroups, leading them to conjecture that such groups are hyperbolic. In this talk, I will confirm and strengthen this conjecture, providing some applications.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper | slides )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

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