An Introduction to Relatively Hyperbolic Groups - Page, Murphy. (2017)
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 $δ$-hyperbolic graphs. We also go over the definition using geometrically finite convergence groups. Finally, 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.