Connecting essential triangulations II: via 2-3 moves only
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910636477251584 |
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| author | Kalelkar, Tejas Schleimer, Saul Segerman, Henry |
| author_facet | Kalelkar, Tejas Schleimer, Saul Segerman, Henry |
| contents | In previous work we showed that for a manifold $M$, whose universal cover has infinitely many boundary components, the set of essential ideal triangulations of $M$ is connected via 2-3, 3-2, 0-2, and 2-0 moves. Here we show that this set is also connected via 2-3 and 3-2 moves alone, if we ignore those triangulations for which no 2-3 move preserves essentiality. If we also allow V-moves and their inverses then the full set of essential ideal triangulations of $M$ is once again connected. These results also hold if we replace essential triangulations with $L$-essential triangulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connecting essential triangulations II: via 2-3 moves only Kalelkar, Tejas Schleimer, Saul Segerman, Henry Geometric Topology 57K31, 57Q15 In previous work we showed that for a manifold $M$, whose universal cover has infinitely many boundary components, the set of essential ideal triangulations of $M$ is connected via 2-3, 3-2, 0-2, and 2-0 moves. Here we show that this set is also connected via 2-3 and 3-2 moves alone, if we ignore those triangulations for which no 2-3 move preserves essentiality. If we also allow V-moves and their inverses then the full set of essential ideal triangulations of $M$ is once again connected. These results also hold if we replace essential triangulations with $L$-essential triangulations. |
| title | Connecting essential triangulations II: via 2-3 moves only |
| topic | Geometric Topology 57K31, 57Q15 |
| url | https://arxiv.org/abs/2407.16509 |