An Investigation Of Weak Amenability Of Hyperbolic Groups
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The purpose of this thesis is to prove that countable finitely-generated hyperbolic groups are weakly amenable. Precisely, the definition of weak amenability is as follows: Let \Gamma be a countable discrete group. We say \Gamma is weakly amenable with constant C if there exist a sequence of finitely supported functions from \Gamma to the complex numbers which converge pointwise to 1, and the CB-norms are uniformly bounded above by C. We interpret weak amenability as there exists an approximate identity whose CB-norm is uniformly bounded by C. The proof of the statement actually draws on many areas of mathematics. In this thesis, we give a quick treatment of the necessary background information before moving onto the associated propositions, lemmas, and theorems used in the proof.
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Copyright © 2021 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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