View AbstractAbstract: In this talk we will give a complete count of the connected components of the character variety of representations of a closed surface group into SO(p,q). In particular, we will exhibit the existence of "exotic" connected component which are not labeled by a characteristic class of SO(p,q) bundles. Each of these exotic components is parameterized by the space of K^p-twisted SO(1,q-p+1) Higgs bundles with the vector space of holomorphic differentials of degree 2,4,...,2n-2. From this parameterization, the Betti numbers for q=p+1 and q=p+2 can be computed. In the end, we will give evidence that these new connected components consist entirely of geometrically interesting (Anosov) representations.