Topology and Geometric Group Theory Seminar

Daniel StudenmundBinghamton
Vanishing in top-dimensional cohomology of GL_n(O)

Tuesday, December 15, 2020 - 1:30pm
Via Zoom

In this talk, we will address one instance of the general question: Given a group G, in which dimensions does G have nontrivial cohomology with rational coefficients? A celebrated result of Borel and Serre implies that G = GL_n(O) has finite virtual cohomological dimension (vcd) when O is the ring of integers of a number field K. This means that cohomology with rational coefficients vanishes in dimensions greater than the vcd, but leaves open the question of whether cohomology vanishes in the vcd. After reviewing Borel and Serre's work and stating related results, I will present joint work with Andy Putman which determines conditions on the number ring O that guarantee vanishing of cohomology of GL_n(O) in the vcd.

Introductory talk at 1:30pm by Yun Liu Seminar talk at 2pm.