"Geometry and Analysis on Groups" Research Seminar

Time: 2016.06.08, 13:00–15:00
Location: 2.Stock Besprechungsraum, Oskar-Morgenstern-Platz 1
Title: "Classifying spaces for families of subgroups for systolic groups."
Speaker: Damian Osajda (Uniwersytet Wrocławski)
Abstract: This is joint work with Tomasz Prytula (Kopenhagen). For a given group $$G$$ a family of its subgroups is a collection of subgroups which is closed under taking subgroups and conjugations by elements of $$G$$. Examples are: the family consisting of only the trivial group, the family of finite subgroups, the family of virtually cyclic subgroups. A classifying space for a given family is a $$G$$-$$CW$$–complex with stabilizers in the family and such that the fixed point set of any subgroup in the family is contractible. Our main result is a construction of low-dimensional classifying spaces for the family of virtually cyclic subgroups for groups acting properly on systolic complexes. Such spaces are of interest in view of their appearance on the left-hand side of the assembly map in the formulation of the Farrell-Jones conjecture. The main technical result is the determination of the large-scale structure of the minimal displacement set of a hyperbolic isometry of a systolic complex. As an application one gets a construction of corresponding low-dimensional classifying spaces for groups acting properly on graphical small cancellation complexes. I will mention other applications.