Abstract
Many useful techniques in group theory have been originally developed for the purpose of studying problems regarding subgroups of free groups and their ranks. An illustrative example is a conjecture attributed to Scott, solved by Bestvina and Handel, which bounds the rank of the subgroup fixed by any automorphism. We will discuss a new approach to this problem based on L2-homology.
Talk
is a finitely generated free group
- All spubgroups of are free
- The intersection of finitely generated subgroups is finitely generated
- For a given Automorphism the subgroup of fixed points is finitely generated (Gersten 1987)
- Friedman, Mineyev 2011 proved an inequality for subgroups
- There is a rank inequality given by Bestvina-Handel 1992 (This was proven using train tracks)
We will try to prove the last inequality using a new approach (Linnells division ring): The group satisfies the Atiyah conjecture so its Linnell’s ring is a division ring.
About
Slowlz revealing part of the proof