Rigidity of Vertex-Regular Actions on Fuchsian Buildings

Graduate Thesis Or Dissertation

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

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Attribute Name	Values
Creator	Smith, Samantha T.
Abstract	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.
License	All rights reserved
Resource Type	Dissertation
Date Issued	2018-07-30
Degree Level	Doctoral
Degree Name	Doctor of Philosophy (Ph.D.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2019
Advisor	Bogley, William A.
Committee Member	Escher, Christine Garity, Dennis Kong, Wei Pengelley, David
Academic Affiliation	Mathematics
Subject	Presentations of groups (Mathematics) Buildings (Group theory)
Urheberrechts-Erklärung	In Copyright
Related Items	Torsion-Free Vertex-Regular Lattices of I55
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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Miniaturansicht	Titel	Hochladedatum	Sichtbarkeit	Aktionen
	SmithSamanthaT2018.pdf	2018-08-05	Öffentlich	Herunterladen
	SmithSamanthaT2018_Appendix.pdf	2018-08-05	Öffentlich	Herunterladen