Representation varieties of twisted Hopf links
\'Angel Gonz\'alez-Prieto, Vicente Mu\~noz
TL;DR
This paper investigates the $SL_r(C)$-representation varieties of twisted Hopf links, providing a general framework and explicit formulas for ranks 2 and 3, combining combinatorics and equivariant Hodge theory.
Contribution
It introduces a new framework for analyzing representation varieties of twisted Hopf links and derives explicit formulas for their E-polynomials in specific ranks.
Findings
Explicit formulas for E-polynomials of rank 2 and 3
A combinatorial and Hodge-theoretic approach to representation varieties
Framework applicable to twisted Hopf links with n twists
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 -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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Algebraic structures and combinatorial models