We study the local structure of the representation variety of a knot group into the special linear
group of degree
over the complex numbers at certain diagonal representations. In particular we
determine the tangent cone of the representation variety at these diagonal
representations, and show that the latter can be deformed into irreducible
representations. Furthermore, we use Luna’s slice theorem to analyze the local
structure of the character variety.
Keywords
knot group, variety of representations, deformations of
reducible representations