The ${\rm SL}(2,\mathbb{C})$-character variety of the magic $3$-manifold

Haimiao Chen

The ${\rm SL}(2,\mathbb{C})$-character variety of the magic $3$-manifold

Geometric Topology 2026-04-08 v1

Authors: Haimiao Chen

Abstract

We determine the irreducible ${\rm SL}(2,\mathbb{C})$ -character variety of the 3-chain link exterior which is called the `magic $3$ -manifold', and deduce a formula for the twisted Alexander polynomial associated to each ${\rm SL}(2,\mathbb{C})$ -representation.

Keywords

SL(2,C)-character variety magic 3-manifold 3-chain link exterior twisted Alexander polynomial representation

Cite

@article{arxiv.2604.05957,
  title  = {The ${\rm SL}(2,\mathbb{C})$-character variety of the magic $3$-manifold},
  author = {Haimiao Chen},
  journal= {arXiv preprint arXiv:2604.05957},
  year   = {2026}
}

Comments

13 pages, 2 figures

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