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

Yi Xie; Boyu Zhang

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

Geometric Topology 2021-05-27 v2

Authors: Yi Xie , Boyu Zhang

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.

Keywords

link groups SU(2) representations meridian-traceless irreducible representations Hopf link knot theory

Cite

@article{arxiv.2104.04839,
  title  = {On meridian-traceless SU(2)-representations of link groups},
  author = {Yi Xie and Boyu Zhang},
  journal= {arXiv preprint arXiv:2104.04839},
  year   = {2021}
}

Comments

39 pages, 28 figures

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