Category Archives: Uncategorized

Today’s lecture was held outside, in the lovely warmth and sunlight. We considered two ways to approach the following statement. Claim. If , then is free. A Geometric Group Theory Proof Instead of proving this claim directly, we started with … Continue reading →

I’ll begin my second (!) blog post about free groups by recalling a proposition that cuts right to the heart of what a free group is. Universal property. Let be a generating set. Then is the unique froups os that … Continue reading →

Monday’s class brought us back to a claim we made last Wednesday, before our fun Coxeter group excursion. MurphyKate noted that this problem showcased a few things: notably free groups being sneaky and hiding in places we might not expect, … Continue reading →

Free groups are a wonderful source of examples, counterexamples, and play a crucial role in some pretty slick constructions. For instance, the famous Banach-Tarski paradox utilizes a construction which, at its heart, boils down to a fact about free groups, … Continue reading →

Class got a bit more technical on this fine Friday morning! We began with Cayley’s Good Theorem and went into details about graph theory. Furthermore, we learned about fundamental domains as a building block to representing infinite groups through graphs.Cayley’s … Continue reading →

Wednesday’s class was a review of groups, a “whirlwind-review” of the basics of graphs and trees, and a look at actions on symmetry groups of geometric object.  Groups, Reviewed To begin with, we reviewed group presentations, of form . For … Continue reading →

Welcome to Geometric Group Theory! As today was the first day of class we began by reviewing the syllabus and discussing expectations for the term before diving into the material. Review of Groups Definition: A group is a set with … Continue reading →

The majority of this page will be a student-generated repository of class notes for a class on Geometric Group Theory, taught primarily from John Meier’s Groups, Graphs, and Trees. You can find the course information (including a syllabus and information … Continue reading →