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Author Archives: Shuhang Xue
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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-Hyperbolicity is Quasi-Isometric Invariant
On Wednesday, when we introduced delta-hyperbolicity, we used the usually Cayley graph of (triangles glued to rectangles) as an example. Specifically, triangles in are 2-slim so that is 2-hyperbolic. On the other hand, we note that -hyperbolicity is a generalization … Continue reading
The Mystery of a Presentation of BS(1,2)
On Friday, Professor Alden Walker gave a lovely talk on the Baumslag-Solitar Groups. I was fascinated by the Cayley graph of . Also, he discussed geodesics between group elements (a shortest but not necessarily unique! path in its Cayley graph … Continue reading
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Week 2, Existence of Fundamental Domain and Some Applications
In this blog, we aim to show 1) the existence of fundamental domains, 2) fundamental domains in Cayley graphs, and 3) a one-to-one correspondence between the transversal of subgroups and components of a fundamental domain of subgroups. 1. Existence of … Continue reading
