MTH425 Geometric Group Theory
Announcements: Important announcements regarding exams, HW etc will be posted here.
Textbooks and references:
1) Bridson, M. R.; Haefliger, A.: Metric spaces of non-positive curvature
2) Cornelia Drutu; Michael Kapovich: Geometric Group Theory
3) Matt Clay; Dan Margalit et al: Office hours with a geometric theorist
Syllabus etc from the institute course page:
MTH425: Geometric group theory
[Cr:4, Lc:3, Tt:1, Lb:0]
Course Outline
Free groups, group presentations, Cayley graphs.
Amalgamated free products and HNN extensions.
Structure of a group acting on a tree.
Ends of a group.
Group actions and quasi-isometries.
Hyperbolic spaces. Hyperbolic groups.
Growth of groups. Polynomial, sub-exponential, exponential growth of groups. Gromovs theorem on groups of polynomial growth.
Grigorchuk group.
Subgroup growth of free groups.
Recommended Reading
Bowditch, B. H.: A course on geometric group theory, MSJ Memoirs, Mathematical Society of Japan, Volume 16, 2006.
Bridson, M. R.; Haefliger, A.: Metric spaces of non-positive curvature, Grundlehren der mathematischen Wissenschaften, Volume 319, Springer, 1999.
Ghys, E.; de la Harpe, P.; Editors: Sur les Groupes Hyperboliques dapr‘es Mikhael Gromov, Progress in mathematics, Birkh�user, 1990.
Pierre de la Harpe: Topics in Geometric Group Theory, Chicago Lectures in Mathematics, The University of Chicago Press, 2000.
Alexander Lubotzky, Dan Segal. Subgroup Growth. Birkhuser, 2003.
Mann, A.: How groups grow, London Mathematical Society Lecture Note Series 395, Cambridge University Press, 2012.
Prerequisites:
Point set topology, metric spaces, covering spaces, fundamental groups. Knowledge of Riemann geometry is helpful but not mandatory. Principles of mathematical analysis- Rudin's first six chapters is essential. Basic knowledge of group theory is essential too.
Exams and quizzes: There will be assignments, presentations and quizzes for evaluation.
Grade distribution: To be announced later.
Homework assignments and presentation topics: To be posted here.
IISER Mohali Academic Calendar: https://www.iisermohali.ac.in/files/pdf/DeanAcad/MS20%20batch.pdf