High-dimensional components of ${\rm SL}(2,\mathbb{C})$-character varieties of prime knots

Haimiao Chen

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arXiv · 2512.13375

High-dimensional components of ${\rm SL}(2,\mathbb{C})$-character varieties of prime knots

Haimiao Chen

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Abstract

For a prime knot $K$, we give sufficient conditions for the existence of a component $\mathcal{C}$ of the irreducible ${\rm SL}(2,\mathbb{C})$-character variety of $K$ with $\dim\mathcal{C}>1$, and give a lower bound for $\dim\mathcal{C}$. Specifically, we improve a result of Paoluzzi and Porti on Montesinos knots, and positively answer a question posed by Culler and Dunfield in 2018.

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Haimiao Chen. 2025-12-15. High-dimensional components of ${\rm SL}(2,\mathbb{C})$-character varieties of prime knots. https://arxiv.org/abs/2512.13375

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