Representation spaces of Seifert fibered homology spheres

Let Σ be a Seifert fibered homology sphere and τ the complex conjugation involution on Σ viewed as a link of singularity. We study the equivariant topology of SU(2) representation space of π1(Σ) with respect to the involution induced by τ. As an application we prove splicing additivity in the Floer homology of Seifert fibered homology spheres.