Proves that the Goeritz group of genus g≥3 Heegaard splittings of S^3 is generated by four elements, using topological minimality.
Powell moves and the Goeritz group
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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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math.GT 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A proof of Powell's conjecture on the Goeritz group of $S^3$
Proves that the Goeritz group of genus g≥3 Heegaard splittings of S^3 is generated by four elements, using topological minimality.