  The genus-$g$ Goeritz group is the group of isotopy classes of
orientation-preserving self-homeomorphisms of the $3$-sphere that preserve the
genus-$g$ Heegaard splitting of the $3$-sphere. In 1933, Goeritz found first a
finite generating set of the genus-$2$ Goeritz group. The Powell Conjecture
offers four specific elements that suffice to generate higher genus Goeritz
group. We show that the reducing sphere complexes for the higher genus
splittings of the $3$-sphere are all connected, and consequently the conjecture
is true.
