Representation varieties of twisted Hopf links

Abstract

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 $S{L}_r(C)$-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.

arXiv comment25 pages, 3 figures; v2. Corrected mistake in the E-polynomial in main theorem

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Cited by in corpus (1)

• The $\mathrm{SL}(2,\mathbb{C})$-character variety of the Borromean link