Primitive tuning via quasiconformal surgery

Using quasiconformal surgery, we prove that any primitive, postcritically-finite hyperbolic polynomial can be tuned with an arbitrary generalized non-escaping critical points, generalizing a result of Douady-Hubbard for quadratic polynomials to the case higher degree polynomials. This solves affirmatively conjecture by Inou and Kiwi on surjectivity renormalization operator in one complex variable.