One Powell generator is redundant

Abstract

In 1980 J. Powell [Trans. Amer. Math. Soc. 257 (1980), pp. 193–216] proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of S 3 S^3 . This conjecture remains unresolved for genus g ≥ 4 g \geq 4 . Here a short argument shows that one of his proposed generators is redundant, in fact a consequence of three of the other four.