One Powell generator is redundant
arXiv:1908.00479
summary
The paper demonstrates that one of Powell's five proposed generators for the Goeritz group of any Heegaard splitting of the 3‑sphere is redundant, as it can be derived from three of the remaining generators.
Abstract
In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of $S^3$. This conjecture remains unresolved for genus $g \geq 4$. Here a short argument shows that one of his proposed generators is redundant, in fact a consequence of three of the other four.
4 pages, 3 figures
Topics & keywords
#goeritz group#heegaard splitting#mapping class group#3-manifolds#group generatorsPowell generatorsredundant generatorgenusS^3Goeritz group