Hyperbolically embedded subgroups in terms of Fine graphs

Rashid, Farhan (2020) Hyperbolically embedded subgroups in terms of Fine graphs. Masters thesis, Memorial University of Newfoundland.

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Abstract

Since the 1980s, mathematicians have been studying hyperbolic groups, and hyperbolic geometry has been considered one of the most useful tools in geometric group theory. In the 2000s, a generalization of hyperbolic groups was introduced by Dahmani, Guiraldel and Osin, known as hyperbolically embedded subgroups. This notion has several applications in group theory and low dimensional topology. In this thesis, we introduce an alternative definition of hyperbolic embedded subgroup modelled on a characterization of a relatively hyperbolic group by Bowditch [2] and prove that our notion is equivalent to the original definition.

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