Varieties of representations and their cohomology-jump subvarieties for knot groups

This paper studies the spaces of representations of knot groups into a linear group $\mathrm{GL}_n(\mathbb{C})$, their categorical factor-spaces (i.e., the spaces of all characters of the representations), and their cohomology-jump subspaces. Connections are established between the latter and the spaces of representations of dimension one greater. A complete description is given of these spaces for 2-bridge knots.