Generating the Goeritz group of $S^3$
Geometric Topology
2024-08-26 v4
Abstract
In 1980 J. Powell \cite{Po} proposed that five specific elements sufficed to generate the Goeritz group for any genus Heegaard splitting of the 3-sphere. Here we prove that a natural expansion of Powell's proposed generators, to include all eyeglass twists and all topological conjugates of Powell's generators does suffice.
Cite
@article{arxiv.2011.10613,
title = {Generating the Goeritz group of $S^3$},
author = {Martin Scharlemann},
journal= {arXiv preprint arXiv:2011.10613},
year = {2024}
}
Comments
v.4 contains minor clarifications throughout. To appear in Journal of the Association for Mathematical Research