Holonomy perturbations in instanton gauge theory and irreducible SL(2,C)-representations of integer homology spheres I

We use the technique of holonomy perturbations in instanton gauge theory, which can be traced back
to Floer and Taubes, to prove some topological results about the image of the representation variety
of the complement of a non-trivial knot in the representation variety of its boundary torus.

The first part discusses some of our recent results and how these imply that integer homology 3-spheres
different from the 3-sphere admit irreducible representations of their fundamental group in SL(2,C),
using a result of Boileau, Rubinstein, and Wang.