English

Powell moves and the Goeritz group

Geometric Topology 2018-04-18 v1

Abstract

In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of S3S^3, extending work of Goeritz on genus 22 splittings. Here we prove that Powell's conjecture was correct for splittings of genus 33 as well, and discuss a framework for deciding the truth of the conjecture for higher genus splittings.

Cite

@article{arxiv.1804.05909,
  title  = {Powell moves and the Goeritz group},
  author = {Michael Freedman and Martin Scharlemann},
  journal= {arXiv preprint arXiv:1804.05909},
  year   = {2018}
}

Comments

39 pages; 17 figures

R2 v1 2026-06-23T01:25:31.743Z