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Abstract: We look at a few of the various ways in which relatively hyperbolic groups are defined. It has been shown that, if a little care taken with hypotheses, all definitions are equivalent; here we examine the relationship between the definitions using the coned-off Cayley graph and fine $\delta$-hyperbolic graphs. We also go over the definition using geometrically finite convergence groups. ... read moreFinally, we use the free group $F_2$ as an example of a relatively hyperbolic group to explore the different definitions.
Thesis (M.S.)--Tufts University, 2017.
Submitted to the Dept. of Mathematics.
Advisor: Genevieve Walsh.
Committee: Kim Ruane, and Robert Kropholler.
Keywords: Mathematics, and Theoretical mathematics.read less