Representation Varieties of Twisted Hopf Links

Abstract

In this paper, we study the representation theory of the fundamental group of the complement of a Hopf link with n twists. A general framework is described to analyze the $${{\,\textrm{SL}\,}}_r({\mathbb {C}})$$ SL r ( C ) -representation varieties of these twisted Hopf links as byproduct of a combinatorial problem and equivariant Hodge theory. As application, close formulas of their E-polynomials are provided for ranks 2 and 3, both for the representation and character varieties.