MA4H4 : Geometric group theory (Old webpage)

I am no longer lecturing this course and the syllabus has changed.
Please check the official course websites for relevant information.

The following information relates to earlier years.

Notes

The following supplement the material of my MSJ notes.

Part 1 Supplement to Section 6 (word problem).
Part 2 First part of Section 7 (isoperimetric stuff).
Part 3 Second part of Section 7.

Exercise sheets

Prepared with the help of Robert Tang.

Sheet 1
Sheet 2
Sheet 3
Sheet 4
Sheet 5
Sheet 6

Solutions prepared by tutors of support classes.

Solution Sheet 1
Solution Sheet 2
Solution Sheet 3
Solution Sheet 4
Solution Sheet 5
Solution Sheet 6

Books

General

B.H. Bowditch [me]: A course on geometric group theory. MSJ Memoirs Volume 16. Mathematical Society of Japan, 2006.
[These are the notes of a course I gave in Tokyo. They will cover a large chunk of the course.]

C. Löh, Geometric group theory, an introduction : Universitext, Springer (2017).

P. de la Harpe, Topics in geometric group theory : Chicago lectures in mathematics, University of Chicago Press (2000).
[Includes many interesting topics in GGT.]
[A general introductory text.]

M. Bridson, A. Haefliger, Metric spaces of non-positive curvature : Grundlehren der Math. Wiss. No. 319, Springer (1999).
[Not an introduction to GGT as such, but it has accounts of many of the main topics we will be covering.]

C. Druţu, M. Kapovich, Geometric group theory : Colloquium publications, Vol. 63, American Mathematics Society (2018).
[A fairly comprehensive reference book on GGT: 819 pages.]

W. Magnus, A. Karrass, D. Solitar, Combinatorial group theory: presentations of groups in terms of generators and relations : Interscience (1966).
[A more traditional approach to combinatorial group theory.]

R.C. Lyndon, P. Schupp, Combinatorial group theory : Springer (1977).
[Ditto.]

E.Ghys, A.Haefliger, A.Verjovsky, (eds.) Group theory from a geometrical viewpoint World Scientific.
[The "Trieste notes". A collection of articles, some expository, from the early days of GGT. The paper version is long out of print, but now available as an ebook, it seems.]

Books/articles on hyperbolic groups.

Several accounts were written around, or shortly after, Gromov's paper. There's been no systematic general introduction since (for some reason).

E.Ghys, P. de la Harpe eds. Sur les groupes hyperboliques d'après Mikhael Gromov : Progress in Mathematics No. 83, Birkhauser (1990).
[The most commonly cited introduction. Mostly in French.]

M.Coornaert, T.Delzant, A.Papadopoulos, Les groupes hyperboliques de Gromov : Lecture notes in Mathematics No. 1441, Springer Verlag (1990).
[Another perspective. Also in French...]

See also the notes by Short et al, and by Bowditch (me) in the Trieste notes above.

Web links

Jon McCammond's Geometric group theory page lists lots of famous people, conferences, etc.

A truncated icosidodecahedron (The Cayley graph of the isosahedral group after collapsing double edges.)

Hyperbolic planar tessellations by Don Hatch (celebrated composer of Manfred the murderer).

Tessellations of hyperbolic 3-space by Roice Nelson. The tessellation arising from Seifert-Weber space is (5,3,5).