Representation spaces of pretzel knots

Abstract

We study the representation spaces $R(K;\mathbf{i})$ as appearing in Kronheimer and Mrowka's framed instanton knot Floer homology, for a class of pretzel knots. In particular, for pretzel knots $P(p,q,r)$ with $p,q,r$ pairwise coprime, these appear to be non-degenerate and comprise representations in SU(2) that are not binary dihedral.

30 pages, 3 figures. This is the published version. It is more general than the previous version regarding the values $p,q,r$. Furthermore, rewritten according after referee's remarks

References in corpus (3)

• Knot homology groups from instantons
• Knots, sutures and excision
• Khovanov homology of alternating links and SU(2) representations of the link group

Cited by in corpus (7)

• The pillowcase and perturbations of traceless representations of knot groups
• A class of knots with simple $SU(2)$ representations
• Traceless SU(2) representations of 2-stranded tangles
• On spectral sequences from Khovanov homology
• Link homology and equivariant gauge theory
• Tracefree $\mathrm{SL}(2,\mathbb{C})$-representations of Montesinos links
• Remarks on SU(2)-simple knots and SU(2)-cyclic 3-manifolds