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arxiv 1804.05909 v1 pith:Z65YCGM4 submitted 2018-04-16 math.GT

Powell moves and the Goeritz group

classification math.GT
keywords genusgoeritzpowellsplittingsconjecturegroupcorrectdeciding
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A proof of Powell's conjecture on the Goeritz group of $S^3$

    math.GT 2026-05 unverdicted novelty 8.0

    Proves Powell's conjecture that the Goeritz group for genus g≥3 Heegaard splittings of S³ is generated by four elements, using the topological minimality of the Heegaard surface.

  2. A proof of Powell's conjecture on the Goeritz group of $S^3$

    math.GT 2026-05 unverdicted novelty 7.0

    Proves that the Goeritz group of genus g≥3 Heegaard splittings of S^3 is generated by four elements, using topological minimality.