Graduate Thesis Or Dissertation

 

Rigidity of Vertex-Regular Actions on Fuchsian Buildings Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/p8418t250

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  • We present a method by which torsion-free groups of automorphisms of a 2-dimensional hyperbolic building which act simply transitively on the vertex set can be constructed, and prove that any such group can be obtained by this construction. The method produces groups defined by finite presentations with strong small cancellation properties, and we prove that when the building is Fuchsian with a regular fundamental chamber, two such groups are isomorphic if and only if there is an isomorphism taking generators to generators and relators to relators. Using these results, we find and classify all the torsion-free vertex-regular groups of automorphisms of Bourdon's building I55.
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