Floer homology for knots and SU(2)-representations for knot complements and cyclic branched covers

in this article, using 3-orbifolds singular along a knot with underlying space a homology sphere Y-3, the question of existence of non-trivial and non-abelian SU(2)-representations of the fundamental group of cyclic branched covers of Y-3 along a knot is studied. We first use Fleer Homology for knots to derive an existence result of non-abelian SU(2)-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian SU(2)-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in S-3.