Baumslag-Solitar groups, automorphisms and generalisations

Abstract: Baumslag-Solitar groups are a well known family in geometric group theory, providing useful (counter)examples - such as groups that are Hopfian but not residually finite. Recently, Ian Leary and Ashot Minasyan introduced a generalisation, finding even more counterexamples - notably groups that are \(\CAT(0)\) but not biautomatic. Outer automorphism groups of Baumslag-Solitar groups range from finite to not even finitely generated, with proofs (and re-proofs) across several authors and years.

In this talk I will summarise (some) of what is known about the automorphisms of Baumslag-Solitar groups, and the more modern, Bass-Serre theoretic techniques that can be used to prove them. I'll then discuss my work with Sam Hughes to extend these results to the automorphisms of Leary-Minasyan groups.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

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.