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

• DOI: 10.1016/j.aim.2023.108947
• Publication Date: 2023-03-08T16:37:15Z
• Authors: Yi Xie; Boyu Zhang
• Keywords: Mathematics - Geometric Topology; 57K10, 57R58; FOS: Mathematics; Geometric Topology (math.GT); 0101 mathematics; 01 natural sciences

39 pages, 28 figures<br/>Suppose L is a link in $S^3$. We show that $��_1(S^3-L)$ 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, $��_1(S^3-L)$ 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.<br/>