Subgroups of Hyperbolic Groups in Dimension at most Two

Eduardo Martinez Pedroza (Memorial University)

Resumen: A result of Gersten states that if G is a hyperbolic group with integral cohomological dimension two, then every finitely presented subgroup of G is hyperbolic. The talk is centered about a recent generalization of Gersten's result for the case that G has rational cohomological dimension 2. The new result applies to a class of torsion-free hyperbolic groups that have integral cohomological dimension three and rational cohomological dimension two discovered by Bestvina and Mess. In the spirit of the seminar, the talk will explain all terminology to understand the result, and describe some of the techniques that were used to prove it. This was joint work with Shivam Arora.