Representation spaces of pretzel knots

preprint2012arXivOpen access

Abstract

We study the representation spaces R(K;i)R(K;\bf{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)P(p,q,r) with p,q,rp, q, r pairwise coprime, these appear to be non-degenerate and comprise representations in SU(2) that are not binary dihedral.

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