Title: The Eilenberg-Ganea problem and groups acting on trees
Speaker: Luis Jorge Sanchez Saldana, OSU
Abstract: In this talk we will define geometric and cohomological dimension for groups relative to a family of subgroups. Next, we will enunciate an Eilenberg-Ganea type theorem in this context, proved y W. Lück and D. Meintrup. This theorem claims that both dimensions are equal if the cohomological dimension is at least 3 or the geometric dimension is at least 4. The Eilenberg-Ganea problem for families is the question of whether both dimensions always coincide. N. Brady, I. Leary, and B. Nucinkis constructed examples of groups with cohomological dimension 2 and geometric dimension 3 with respect to the family of finite subgroups. We will discuss how to construct more examples using known examples of groups with cohomological dimension 2 and geometric dimension 3 for a given family, and Bass-Serre theory.
