On meridian-traceless SU(2)-representations of link groups

Yi Xie; Boyu Zhang

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arXiv · 2104.04839

On meridian-traceless SU(2)-representations of link groups

Yi Xie·Boyu Zhang

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Abstract

Suppose L is a link in $S^3$. We show that $\pi_1(S^3-L)$ admits an irreducible meridian-traceless representation in SU(2) if and only if L is not the unknot, the Hopf link, or a connected sum of Hopf links. As a corollary, $\pi_1(S^3-L)$ admits an irreducible representation in SU(2) if and only if L is neither the unknot nor the Hopf link. This result generalizes a theorem of Kronheimer and Mrowka to the case of links.

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Yi Xie, Boyu Zhang. 2021-04-10. On meridian-traceless SU(2)-representations of link groups. https://arxiv.org/abs/2104.04839

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