Author Archives: Michaela Polley

Motivation and Definition When we studied free products, we discussed the free product with amalgmation very briefly. To recall, given two groups and , with subgroups and and an isomorphism ; the free product of and , amalgamating the subgroups … Continue reading →

Hyperbolic Groups The next thrust of the course is hyperbolic groups. We care about hyperbolic groups for four reasons: In many models of “random groups,” groups are hyperbolic with probability 1. For example, under the few-relators model of random groups, … Continue reading →

Today we discussed a new way to combine two groups: the Free Product, and looked at the Cayley Graph of such products which led us to discuss Bass-Serre Trees. The Free Product of Groups Definition. Let and be groups. The … 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 →