PDF Version: A PDF version of this syllabus is available
Office hours. T 8:30-9:20, W 9-10:50 and by appointment in SH 6711
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Course Home Page.
No required text, but three books are
recommended as being quite good: ``Reflection groups and Coxeter
groups'' by Humphreys (1990), ``Combinatorics of Coxeter groups'' by
Bjoerner and Brenti (2005), and ``The Geometry and Topology of Coxeter
Groups'' by Davis (2008).
Course description. Math 227 is a topics course in topology,
broadly defined. The topic changes from quarter to quarter. This
quarter the focus is on the geometry, topology and combinatorics of
Coxeter groups and reflection symmetries. After a detailed
consideration of the motivating cases of spherical and euclidean
discrete reflection groups, the general theory of Coxeter groups will
be discussed with a focus on their standard faithful linear
representations and the nonpositively curved piecewise euclidean
complexes on which they act geometrically.
Grading. Your grade will primarily determined by attendance,
participation, and the extent to which you complete the various short
assignments given out during the course. As befits a third-year
graduate course, the primary focus will be on the material itself
rather than the grading.
Copyright Information. Please note that all written and web
materials for this course have an implied copyright. In particular,
you can download (or xerox) for your own use, but you may not
reproduce them for others.