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

Abstract

Suppose L is a link in S 3 . We show that π 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, π 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 [KM10b, Corollary 7.17] to the case of links.

An enhanced Euler characteristic of sutured instanton homology

“…In [LY21], the authors of the current paper studied the Euler characteristics of this decomposition of SHIpM, γq and related it to the Euler characteristic of SF HpM, γq, which is known as the sutured Floer homology introduced by Juhász, and whose Euler characteristic has been understood by work of Friedle, Juhász, and Rasmussen in [FJR09]. The study of Euler characteristics was further used by the author to compute the instanton Floer homology of some families of p1, 1q-knots in a general lens space and was recently further utilized by Zhang and Xie [XZ21] to prove that links in S 3 all admit irreducible SU p2q representations except for connected sums of Hopf links.…”