The Powell Conjecture for the genus-three Heegaard splitting of the
$3$-sphere
The Powell Conjecture for the genus-three Heegaard splitting of the
$3$-sphere
The Powell Conjecture states that four specific elements suffice to generate the Goeritz group of the Heegaard splitting of the $3$-sphere. We present an alternative proof of the Powell Conjecture when the genus of the splitting is $3$, and suggest a strategy for the case of higher genera.