To be announced.

Group presentations. Cayley graphs. Quasi-isometries. (Fundamental groups and hyperbolic geometry.) Hyperbolic groups. Isoperimetric inequalities. [Other topics depending on time and demand.]

Note, the course was given by a different lecturer last year, and so it may have covered different topics. This year it will revert to a similar syllabus as preceding years.

100% written examination.

You can find past exam papers here:
here.
(You need to log in!)

Note: the 2014 paper was set by a different lecturer, and based
on a slightly different syllabus.

These are the 2010 versions, as handed out in lectures.

Part 1 Supplement to Section 6 (word problem).

Part 2 First part of Section 7 (isoperimetric stuff).

Part 3 Second part of Section 7.

Sheet 1

Sheet 2

Sheet 3

Sheet 4

Sheet 5

Sheet 6

**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.]

P. de la Harpe,
*Topics in geometric group theory*
: Chicago lectures in mathematics, University of Chicago Press (2000).

[Includes many interesting topics in GGT.]

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.]

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.
Out of print, sadly.]

**Books/articles on hyperbolic groups.**

Several accounts were written around shorly 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.

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).

A tessellation of hyperbolic 3-space by right-angled regular dodecaheda. This isn't quite the same the one you get from Seifert-Weber space. That one has five dodecahedra meeting around each edge rather than four.