Hyperbolic group extensions
Introductory Workshop: Geometric Group Theory August 22, 2016  August 26, 2016
Location: SLMath: Eisenbud Auditorium
geometric group theory
hyperbolic groups
Gromov boundary
outer automorphism groups
group extensions
isoperimetric inequalities
20Jxx  Connections of group theory with homological algebra and category theory
00A35  Methodology of mathematics {For mathematics education, see 97XX}
2008  Computational methods for problems pertaining to group theory
20Exx  Structure and classification of infinite or finite groups
14590
William Thurston's seminal construction of a hyperbolic 3manifold fibering over the circle gave the first example of a Gromov hyperbolic surfacebycyclic group. This breakthrough sparked a flurry of activity, and there has subsequently been much progress towards developing a general theory of hyperbolic group extensions. In this talk I will review some of this basic theory  including combination theorems for ensuring a group extension is hyperbolic and structural theorems about general hyperbolic extensions  and then discuss my work with Sam Taylor studying hyperbolicity in the specific context of free group extensions. For instance, we use the geometry of Outer space to show that every purely atoroidal subgroup of Out(F_n) that quasiisometrically embeds into the free factor complex gives rise to a hyperbolic extension of F_n
Dowdall Notes

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