Geometric and asymptotic group theory I
Lecture by Goulnara Arzhantseva
Problem session by Damian Osajda
Dienstag, 10:00--12:00, Raum C2.07 UZA 4
Lists of problems:
Blatt 1, Blatt 2,
Blatt 3, Blatt 4,
Blatt 5, Blatt 6
1st EXAM. January 31 from 17:00 till 18:00, room D107. Note: 20 min preparation, 20 min oral presentation (time is strict !), one A4 format page of "reminder" is allowed.
2nd EXAM. March 13 from 17:00 till 18:00, room C207. Note: 20 min preparation, 20 min oral presentation (time is strict !), one A4 format page of "reminder" is allowed.
References (advised but not obligatory!):
- Free groups, group presentations:
Ch. 2 (pages 52-56, 58-60, 71-74, 81-84) of the book by Oleg Bogopolski, Introduction to group theory
Chapters 1 and 4 of the book by.D.L. Johnson, Presentations of Groups (second edition)
- Van Kampen diagrams:
Hamish Short, Introduction to the geometry of the word problem in "The geometry of the word problem for finitely generated groups", Advanced Courses in Mathematics - CRM Barcelona, 2006.
- Graphical small cancellation:
Yann Ollivier, On a small cancellation theorem of Gromov, Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 1, 75-89.
- Phase transition theorem:
Ch.2, pages 607-615 of Yann Ollivier, Sharp phase transition theorems for hyperbolicity of random groups, GAFA 14 (2004), available at http://www.yann-ollivier.org/rech/publs/quothyp_publ.pdf