Large Scale Geometry of Groups

The course is a slow hike towards the goal to prove quasi-isometric rigidity of free groups (without touching accessibility issues).

The course takes place Monday, Tuesday and Thursday 09:30 -- 10:30. The room is CYCL 05 on Mondays and Thursdays. On Tuesday 17.10. and 07.11., the room is SUD 02, otherwise it is CYCL 03.

The course started in semester week 3 and has 20 single hours in total. There are also no lectures in semester weeks 6, 7, 9 and 14. There is no lecture on December 8, 13 and 15.

Here we provide an outline of the course content and references where the content of the course can be looked up. Some of it might only be accessible via the UCLouvain network (e.g. via VPN). Note that the given material never exactly corresponds to what was done in class, typically there will be more information in the references. If you find references that you find better, I can put them here. If you have any questions or comments, don't hesitate to contact me.

Our main sources will be the following.
Geometric group theory by Clara Löh
Geometric group theory by Cornelia Drutu and Michael Kapovich

Free groups, presentations and Cayley graphs:
In Löh: Section 2.2, Section 3 until and with 3.3.2
In Drutu-Kapovich: Section 7.2, Seciton 7.3, Prop. 7.38, Section 7.4 until and with Example 7.75

Bass-Serre theory:
Article by Garrido, Glasner and Tornier , Section 2.2 explaining the three types of tree automorphisms
See the article by W. Woess for the definition of the diameter of an end that we used.
Short note by W. Yang

Quasi-isometries and the Milnor-Schwarz Lemma:
In Löh: Corollary 5.4.2, Corollary 5.4.7
In Drutu-Kapovich: Thm 8.37, Cor 8.47

Ends:
Notes by Bernhard Krön , without Section 9
See the article by W. Woess for the definition of the diameter of an end that we used.
For 2-ended groups, see the Groups, Graphs and Trees by John Meier, Section 11.6 (we had a different proof in class)

Stallings' End Theorem:
We followed the article by Bernhard Krön .

More groups acting on trees:
Finite generation of amalgamated products, see this stackexchange thread
Characterisation of free groups: Section 4.4.2 in Löh.

Endgame:
In Drutu-Kapovich: Theorem 20.45

Grushko's Theorem:
Article by W. Imrich

Where I didn't find sources reasonably close to the course. I encourage you to search in the literature and tell me if you find something.
Any statement involving the infinite diameter of ends
A group acting on a tree with trivial edge stabilizers and fee vertex stabilizers is free.
In an amalgamated product over a finite group, the base groups are non-distorted.
Amalgamated products of virtually free groups over a finite group are virtually free.