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Author Archives: Michaela Polley
HNN Extensions
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
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Week 7 Monday: Hyperbolic Groups and QuasiIsometry
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 fewrelators model of random groups, … Continue reading
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Week 4 Monday: The Free Product of Groups
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 BassSerre Trees. The Free Product of Groups Definition. Let and be groups. The … Continue reading
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Week 1 Monday: Groups and Group Presentations
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
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