MATH 595
Open problems in group theory and topology,
in the second half of Fall 2018. Starts on Monday, October 22, 2018.
Class time and place: MWF 3.00pm3.50pm
Professor: Igor Mineyev, 243 Illini Hall. It is better to talk to me during and after the class
and to come to office hours rather than to send email. Discussions are more efficient that way.
Office hours: Monday and Wednesday, 1.00pm1.50pm.
Course description.
No prerequisites are required, but it is helpful to have some familiarity with standard notions of group theory/topology/geometry: group, Cayley graph, group presentation, topological space,
cell complex, fundamental group, covering space, etc. There are many sources for this preliminary material, for example:
Homework will appear here.
If a newer version does not show up, restart your browser.
There is no standard textbook for the course.
If you are interested in learning geometric/combinatorial group theory in depth,
here is an incomplete list of books related to the subject, in no particular order.
 Magnus, Karras, Solitar. Combinatorial group theory.
 Lyndon, Schupp. Combinatorial group theory.
 Bridson, Haefliger. Metric spaces of nonpositive curvature.
 Ghys, Haefliger, Verjovsky. Group theory from a geometrical viewpoint.
 Ken'ichi Ohshika. Discrete grops.
 John Meier. Groups, graphs and trees: an introduction to the geometry of infinite groups.
 Colins, Grigorchuk, Kurchanov, Zieschang. Combinatorial group theory and applications to geometry.
 Gersten (editor). Essays in group theory. MSRI publications.
 Ghys, de la Harpe. Sur les groupes hyperboliques d'apres Mikhael Gromov.
 Bedford, Keane, Series (editors). Ergodic theory, symbolic dynamics and hyperbolic spaces.
 Ross Geoghegan. Topological methods in group theory.
 Michael Davis. The geometry and topology of Coxeter groups.
 Pierre de la Harpe. Topics in geometric group theory.
 Epstein (editor), Cannon, Holt, Levy, Paterson, Thurston. Word processing in groups.
 HogAngeloni, Metzler, Sieradski (editors). Twodimensional homotopy and combinatorial group theory.
London Mathematical Society Lecture Note Series, 197.
 Coornaert, Delzant, Papadopoulos. Géométrie et théorie des groupes.
 John Hempel. 3manifolds.
 Kenneth Brown. Cohomology of groups.
 Scott, Wall. Topological methods in group theory.

Drutu, Kapovich. Geometric group theory.
Here are links to interesting open problems. Explore and solve a few.