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.

  • 2
    $\begingroup$ Similar to mathoverflow.net/questions/3858/… $\endgroup$ Commented Jul 8, 2015 at 14:16
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    $\begingroup$ You already mentioned three of my favourites! $\endgroup$
    – HJRW
    Commented Jul 8, 2015 at 21:10
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    $\begingroup$ I hope the question will be closed and remain closed as primarily opinion-based, especially insofar as it potentially means advertising contemporary articles, and given some kind of ranking (in terms of the number of upvotes) of these papers. $\endgroup$
    – YCor
    Commented Jul 9, 2015 at 14:03
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    $\begingroup$ Note that the poster is not asking for the "best" papers, but rather for suggestions of "favorite" papers. I'm very interested in hearing what the experts have to say! $\endgroup$
    – Sam Nead
    Commented Jul 25, 2015 at 21:41

3 Answers 3


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.


This beautiful one page proof of surface groups are residually finite.

  • $\begingroup$ Maybe I am missing something, but I find the first assertion of the second paragraph suspicious. I cannot insert a picture in a comment, but the word $b_1^2a_1b_1^{-1}b_2^{-1}$ in $$\langle a_1,a_2,b_1,b_2 \mid [a_1,b_1][a_2,b_2]=1 \rangle$$ seems to be representable as a non singular loop whereas it is neither a standard generator nor a product of commutators of standard generators. $\endgroup$
    – Seirios
    Commented Jul 28, 2015 at 12:38
  • $\begingroup$ @Seirios see math.stackexchange.com/questions/751823/… for an explanation. $\endgroup$
    – Cusp
    Commented Jul 28, 2015 at 16:59

The paper B. Krön. Cutting up graphs revisited - a short proof of Stallings' structure theorem gives a short and accessible proof of Stalling's End Theorem in full detail.


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