On the deformation theory of representations of fundamental groups of compact hyperbolic 3-manifolds

we construct compact hyperbolic 3-manifolds M1, M2 and an irreducible representation ρ1: π1(M1) → SO(3) so that singularity of the representation variety of π1(M1) into SO(3) at ρ1 is not quadratic. We prove that for any semi-simple Lie group G the singularity of the representation variety of π1(M2) into G at the trivial representation is not quadratic.