Virtually unipotent elements of 3-manifold groups

Abstract: Suppose a group $G$ contains an infinite-order element $g$ such that every finite-dimensional linear representation of $G$ maps some nontrivial power of $g$ to a unipotent matrix. Since unitary matrices are diagonalizable, and since a unipotent matrix is torsion if its entries lie in a field of positive characteristic, such a group $G$ does not admit a faithful finite-dimensional unitary representation, nor is $G$ linear over a field of positive characteristic. We discuss manifestations of the above phenomenon in various finitely generated groups, with an emphasis on 3-manifold groups.

group theorygeometric topologymetric geometry

Audience: researchers in the topic

McGill geometric group theory seminar