Marco Linton

University of Warwick

Hyperbolicity of certain one-relator groups

Algebra Seminar

27th April 2022, 2:30 pm – 3:30 pm
Fry Building, Room 2.04

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/<>. 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 show how to confirm and strengthen this conjecture, providing some applications.

Organisers: Tim Burness, Charles Cox

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