# Topics in Algebra: Coxeter Groups (2022S)

Coxeter groups are abstract reflection groups. Concrete examples include symmetry groups of regular polytopes and the triangle groups that are the symmetry groups of triangular tilings of the sphere, Euclidean plane, and hyperbolic plane.

## Course topics:

- Survey geometric reflection groups.
- Abstract reflection groups and the combinatorial group theory of Coxeter groups.
- Introduction to geometric group theory and construction of the Davis complex for Coxeter groups.
- How cube complexes are better than polyhedral complexes and applications to modern results in right-angled Coxeter groups.

Basic group theory and linear algebra are assumed, but no prior experience in combinatorial or geometric group theory is required.
## Syllabus

Syllabus
## Lecture Notes:

Notes on Coxeter groups
## Exercises:

Exercises appear in the lecture notes.
## Further Literature:

- Michael W. Davis, The geometry and topology of Coxeter groups,
London Mathematical Society Monographs Series, vol. 32, Princeton
University Press, Princeton, NJ, 2008.
- Pallavi Dani, The large-scale geometry of right-angled Coxeter
groups, Handbook of group actions. V, Adv. Lect. Math. (ALM),
vol. 48, Int. Press, Somerville, MA, 2020, pp. 107-141.

## COVID contingency plan

The plan is for this course to meet in-person. If it becomes necessary to move to hybrid or remote instruction due to COVID illnesses/quarantine then the lectures will be livestreamed via Zoom. If this happens you will be notified by email and a link to the Zoom meeting will be added to the Moodle page.

Last updated June 30, 2022.

http://www.mat.univie.ac.at/~cashen/Classes/CoxeterGroups.html