One Powell generator is redundant

2019/07/26 by Scharlemann, Martin
#57N12 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1908.00479

Abstract

In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of S³. This conjecture remains unresolved for genus g ≥ 4. Here a short argument shows that one of his proposed generators is redundant, in fact a consequence of three of the other four.

Related

• Powell moves and the Goeritz group
• Powell's Conjecture on the Goeritz group of S³ is stably true
• The Powell Conjecture for the genus-three Heegaard splitting of the 3-sphere
• Generating the genus g+1 Goeritz group of a genus g handlebody
• On the Invalidity of Lemma 2.5 in our previous work on the Powell Conjecture