# Topology Seminar, Alyson Hildum (Wes): "Right-angled Artin groups with tame cohomology"

Wednesday, November 11, 2015
4:15 PM - 5:15 PM (ET)
Exley Science Center (Tower)
Event Type
Seminar/Colloquium
Contact
Caryn Canalia
Department
Mathematics and Computer Science
Abstract: In this talk we will discuss certain group cohomological conditions arising in the study of 4-manifolds with right-angled Artin fundamental groups. While investigating a 4-manifold classification problem, Ian Hambleton and I discovered an interesting question about the cohomology of right-angled Artin groups (RAAGs) with group-ring coefficients. We call a $G$-module A a torsion module if $Hom_{ZG}(A,ZG)=0$ (where ZG is the group-ring). For any group $G$, the group cohomology group $H^i(G;ZG)$ is a $G$-module, and one can ask under which conditions these cohomology groups are torsion modules. Certain conditions on the cohomology groups (which we call "tame cohomology") allow for a better understanding of the structure of the second homotopy group of a 4-manifold $M$, $\pi_2(M)$, as a $\pi_1(M)$-module, which is necessary for tackling our classification problem.