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

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.

39 pages, 28 figures