Powell's Conjecture on the Goeritz group of $S^3$ is stably true
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908592234299392 |
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| author | Scharlemann, Martin |
| author_facet | Scharlemann, Martin |
| contents | In 1980 J. Powell proposed that, for every genus $g$, five specific elements suffice to generate the Goeritz group $\mathcal {G}_g$ of genus $g$ Heegaard splittings of $S^3$. Powell's Conjecture remains undecided for $g \geq 4$. Let $\mathcal{P}_g \subset \mathcal {G}_g$ denote the subgroup generated by Powell's elements. Here we show that, for each genus $g$, the natural function $\mathcal {G}_g \to \mathcal {G}_{g+1}/\mathcal {P}_{g+1}$ is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13629 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Powell's Conjecture on the Goeritz group of $S^3$ is stably true Scharlemann, Martin Geometric Topology 57K35, 57M50, 57M60 In 1980 J. Powell proposed that, for every genus $g$, five specific elements suffice to generate the Goeritz group $\mathcal {G}_g$ of genus $g$ Heegaard splittings of $S^3$. Powell's Conjecture remains undecided for $g \geq 4$. Let $\mathcal{P}_g \subset \mathcal {G}_g$ denote the subgroup generated by Powell's elements. Here we show that, for each genus $g$, the natural function $\mathcal {G}_g \to \mathcal {G}_{g+1}/\mathcal {P}_{g+1}$ is trivial. |
| title | Powell's Conjecture on the Goeritz group of $S^3$ is stably true |
| topic | Geometric Topology 57K35, 57M50, 57M60 |
| url | https://arxiv.org/abs/2210.13629 |