Powell moves and the Goeritz group

Michael Freedman; Martin Scharlemann

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arXiv · 1804.05909

Powell moves and the Goeritz group

Michael Freedman·Martin Scharlemann

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Abstract

In 1980 J. Powell proposed that five specific elements sufficed to generate the Goeritz group of any Heegaard splitting of $S^3$, extending work of Goeritz on genus $2$ splittings. Here we prove that Powell's conjecture was correct for splittings of genus $3$ as well, and discuss a framework for deciding the truth of the conjecture for higher genus splittings.

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Michael Freedman, Martin Scharlemann. 2018-04-16. Powell moves and the Goeritz group. https://arxiv.org/abs/1804.05909

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