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