Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifolds

Vanni Noferini, Gerald Williams

We study the Smith forms of matrices of the form $f(C_g)$ where $f(t),g(t)\in R[t]$, $C_g$ is the companion matrix of the (monic) polynomial $g(t)$, and $R$ is an elementary diviso…