On the local structure of the SL(n,C)-representation variety of knot groups

2024/04/15 by Heusener, Michael, Abdelghani, Leila Ben
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.09548

Abstract

We study the local structure of the representation variety of a knot group into SL(n,C) 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.

Related

• SL(n,C)- Representation spaces of Knot Groups
• Irreducible representations of knot groups into SL(n,C)
• The SL(3,C)-character variety of the figure eight knot
• Character varieties for SL(3,C): the figure eight knot
• The SL(2,C)-character varieties of torus knots