References References
Much of the material in these lectures is covered in [5], but this book is difficult to read. Stillwell's book [6] has an excellent treatment of algorithmic problems and covers many crucial interactions between topology and group theory that will not be not covered in this course. Both of these books also give important historical accounts.
Although the ideas of small cancellation theory have been around for many decades the paper [7] gives a thorough and modern treatment of the topic. Most material on hyperbolic groups will be taken from [2].
The book, which as of 2020, gives the best description of the field is Drutu and Kapovich's Geometric Group Theory [4]. This book also has many historical references. Many important topics not covered in this book are covered in [3] which is also called... Geometric Group Theory.
As far as accessible contemporary introductions go, the texts [1] and [9] are at a level similar to this course, but cover different topics.(And yes, so far there are three books with the same title.) Office Hours with a Geometric Group Theorist apparently also gives a good idea of the field. And finally [10] is another good introductory text which covers substantially different topics.
[1]
Oleg Bogopolski. Introduction to Group Theory. February 2008.
[2]
J. M. Alonso, T. Brady, D. Cooper, V. Ferlini, M. Lustig, M. Mihalik, M. Shapiro, and H. Short. Notes on word hyperbolic groups. In Group theory from a geometrical viewpoint (Trieste, 1990), pages 3–63. World Sci. Publ., River Edge, NJ, 1991.
[3]
Mladen Bestvina, Michah Sageev, and Karen Vogtmann, editors. Ge- ometric group theory. Number volume 21 in IAS/Park City math- ematics series. American Mathematical Society ; Institute for Ad- vanced Studyb, Providence, RI : [Princeton, N.J.], 2014.
[4]
Cornelia Druţu and Michael Kapovich. Geometric Group Theory. American Mathematical Soc., March 2018.
[5]
Roger C. Lyndon and Paul E. Schupp. Combinatorial group theory. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
[6]
John Stillwell. Classical topology and combinatorial group theory, volume 72 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1993.
[7]
Jonathan P. McCammond and Daniel T. Wise. Fans and Ladders in Small Cancellation Theory.. Proceedings of the London Mathematical Society, 84(3):599–644, May 2002. Publisher: Cambridge University Press.
[8]
Matt Clay and Dan Margalit, editors. Office hours with a geometric group theorist. Princeton University Press, Princeton, NJ, 2017.
[9]
Clara Löh. Geometric group theory. Universitext. Springer, Cham, 2017.
[10]
Vaughn Climenhaga and Anatole Katok. From Groups to Geometry and Back. American Mathematical Soc., April 2017
