Fixed points, splittings and division rings

Abstract: Let $G$ be a free group of rank $N$, let $f$ be an automorphism of $G$ and let $\mathrm{Fix}(f)$ be the corresponding subgroup of fixed points. Bestvina and Handel showed that the rank of $\mathrm{Fix}(f)$ is at most $N$, for which they developed the theory of train track maps on free groups. Different arguments were provided later on by Sela, Paulin and Gaboriau-Levitt-Lustig. In this talk, we present a new proof which involves the Linnell division ring of $G$. We also discuss how our approach relates to previous ones and how it gives new insight into variations of the problem.

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 at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.