%0 Journal Article %T Holomorphic Removability of Julia Sets %A Jeremy Kahn %J Mathematics %D 1998 %I arXiv %X Let $f(z) = z^2 + c$ be a quadratic polynomial, with c in the Mandelbrot set. Assume further that both fixed points of f are repelling, and that f is not renormalizable. Then we prove that the Julia set J of f is holomorphically removable in the sense that every homeomorphism of the complex plane to itself that is conformal off of J is in fact conformal on the entire complex plane. As a corollary, we deduce that the Mandelbrot Set is locally connected at such c. %U http://arxiv.org/abs/math/9812164v1