Holonomy perturbations of traceless SU(2) character varieties tangles in 3 manifolds

With the aim to produce a lagrangian-Floer theory associated to tangle decompositions of links in 3-manifolds, holonomy perturbations of the corresponding flat moduli spaces are needed to make the moduli spaces smooth. I will describe what holonomy perturbations are, some results on smoothing flat moduli spaces of tangles, propose a definition of the associated Floer theory, and give evidence that it coincides with Kronheimer-Mrowka's singular instanton homology.  work in progress with C. Herald and M. Hedden.