English

One Powell generator is redundant

Geometric Topology 2019-08-02 v1

Abstract

In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of S3S^3. This conjecture remains unresolved for genus g4g \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.

Cite

@article{arxiv.1908.00479,
  title  = {One Powell generator is redundant},
  author = {Martin Scharlemann},
  journal= {arXiv preprint arXiv:1908.00479},
  year   = {2019}
}

Comments

4 pages, 3 figures

R2 v1 2026-06-23T10:37:28.263Z