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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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Automaticity of Hyperbolic Groups
This term has been lots of fun! It has been great meeting seven more people who would make great theoretical computer scientists if they really put their hearts into it!
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Residual Finitude and Hyperbolicity!
It’s been a very long but very fun term. Cheers!
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Fuchsian Groups
It’s pronounced fookseean not fyooshun 🙁 Thanks for an awesome class!
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What groups are Amenable, and what are not?
What to continue to learn about amenable groups after my presentation? Hope you will find this reading enjoyable! Finally, it was a good class with you all. I wish everyone a merry holiday season. QED
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Proper(T)
I hope you enjoy reading about Property and expanding graphs! Thank you everyone for making Geometric Group theory a wonderful class!! (Edit: Sorry for the super late update, I meant to do this at the beginning of break but apparently … Continue reading
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9th Friday: CAT(0) Cube Complexes!
Last time we dug into random groups — MurphyKate’s favorite kind of group (until she heard my presentation on braids). We also covered the Gromov density model and small cancellation. Some of the key points picked up can be summed … Continue reading
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Eighth Monday: Geometric Actions and a Schwarz Lemma
On this fine Halloween, we discussed what it means to act geometrically, vindicating our work on hyperbolicity with a discussion of the Schwarz Lemma. First, recall the definition from last week: Definition. A group G is hyperbolic if it acts geometrically … Continue reading
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Hyperbolicity is QuasiIsometric Invariant
On Wednesday, when we introduced deltahyperbolicity, we used the usually Cayley graph of (triangles glued to rectangles) as an example. Specifically, triangles in are 2slim so that is 2hyperbolic. On the other hand, we note that hyperbolicity is a generalization … Continue reading