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SUMMARY:When does a one-relator group have a quasi-convex hierarchy? - Mar
 co Linton (University of Warwick)
DTSTART:20211105T134500Z
DTEND:20211105T144500Z
UID:TALK162487@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Within the class of one-relator groups\, those with torsion ar
 e better understood: they are hyperbolic\, their Magnus subgroups are quas
 i-convex and so they (virtually) have quasi-convex hierarchies. However\, 
 many torsion-free two-generator one-relator groups exhibit pathological be
 haviours. Recently\, Louder and Wilton have shown that one-relator groups 
 with negative immersions do not contain two-generator one-relator subgroup
 s\, leading them to conjecture that such groups are hyperbolic. In this ta
 lk\, I will show how to refine the classical Magnus--Moldavanskii hierarch
 y for a one-relator group. I will show that a one-relator hierarchy withou
 t Baumslag--Solitar subgroups is a hyperbolic quasi-convex hierarchy if it
  satisfies an additional technical hypothesis. I will then relate this wit
 h the conjecture of Louder and Wilton and show how it can be converted to 
 a question about free groups.
LOCATION:In person if possible
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