I would like to improve my "depth of understanding" in geometric group theory. So I am interested in short and accessible papers on subjects related to this field but which are not always available in the classical references.
To make my question more precise: By short, I mean a research paper of at most twenty pages or a book containing at most one hundred pages. By accessible, I mean a(n almost) self-contained paper for postgraduate students.
Here are some examples which I think are suitable:
-
Topology of finite graphs, Stallings (15 pages). One of my favorite papers. Stallings shows how to apply covering spaces to finite graphs in order to prove several non-trivial properties of free groups.
-
Topological methods in group theory, Scott and Wall (about 60 pages). The authors proves several classical results of geometric group theory (Stallings' ends theorem, Grushko's and Kurosh's theorems, Bass-Serre theory) using the formalism of graphs of spaces.
-
Subgroups of surface groups are almost geometric, Scott (12 pages). Peter Scott proves that surface groups are LERF by using hyperbolic geometry.
I hope my question is precise enough to be of interest.
EDIT: I don't think my question is a duplicate of Introductory text on geometric group theory?. Rather, I see it as complementary: I ask about some interesting subjects which are typically not available in these classical references.
Best Answer
Andrezj Zuk's notes on Automata groups gives a nice introduction to the topic computing explicit examples. In particular, his description of the Aleshin group (a finitely generated torsion group) and proof of intermediate growth is quite accessible and somewhat simpler than the proof for Grigorchuk's group.