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I am looking for a self contained survey / paper / lecture notes on small cancellation theory and it's generalizations.

I am aware of Lyndon and Schupp's textbook chapter and I have been recommended Mark Hagen's notes, however, I cannot find a copy online of Hagen's notes. I am interested in any other suggestions.

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  • $\begingroup$ Could you comment more on what you want(Why is Lyndon and Schupp not good for you?). What sort of generalizations are you looking for? Have you looked at references provided say in the wikipedia page? $\endgroup$ – user29123 Apr 19 '19 at 16:33
  • $\begingroup$ I'm not sure how helpful this is but I'm interested in a more recent geometrically flavoured survey, I'm especially interested in applications to $CAT(0)$ groups. I currently do not have access to Lyndon and Schupp so I'm looking for an alternative. $\endgroup$ – Sam Hughes Apr 19 '19 at 16:43
  • $\begingroup$ You could email Mark(or whoever recommended his notes) and see if he has a copy. Not sure how many good notes of more recent incarnations of small cancellation theory there are, especially if it doesn't assume more classical stuff like C'(1/6) and C(6)/intuition. You might have to go to papers. Riches to RAAGS have a section on cubical small cancellation theory, but I havn't read it, but it is worth a look to see if it understandable to you. $\endgroup$ – user29123 Apr 19 '19 at 18:07
  • $\begingroup$ Feel free to put that comment as an answer, I think riches to raags has what I'm looking for. $\endgroup$ – Sam Hughes Apr 19 '19 at 18:21
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Combinatorial group theory by Lyndon and Schupp is the classic text to be introduced to small cancellation groups. There is also Geometry of defining relations in groups by Ol'shanskii which introduces small cancellation theory and has generalizations which where used to prove the existence of Tarski monsters.

For cubical small cancellation Wise has a section in Riches to RAAGS, but I have not read it, but looks pretty good.

Graphical small cancellation Ollivier has a paper On a small cancellation theorem of Gromov which gives a combinatorial proof of the basic small cancellation results, and I think having some knowledge of classical small cancellation theory would make this basically self contained. It is an important step in the proof that there exists finitely generated groups which do not coarsely embed in Hilbert spaces, by being flexible enough to make groups contain a sequence of expanders.

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  • $\begingroup$ Thank you very much! $\endgroup$ – Sam Hughes Apr 19 '19 at 19:07

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