The Lodha--Moore groups and their $n$-adic generalizations are not SCY
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912187307524096 |
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| author | Kodama, Yuya Takano, Akihiro |
| author_facet | Kodama, Yuya Takano, Akihiro |
| contents | A closed 4-manifold is symplectic Calabi--Yau (SCY) if its canonical class is trivial. Friedl and Vidussi proved that Thompson's group $F$ cannot be the fundamental group of any SCY manifold. In this paper, we show that its generalizations, called the Brown--Thompson group and the $n$-adic Lodha--Moore groups, cannot be also the fundamental group of any SCY manifold by using their method. From this proof, we also show that there exist non-trivial infinitely many examples which satisfy Geoghegan's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Lodha--Moore groups and their $n$-adic generalizations are not SCY Kodama, Yuya Takano, Akihiro Geometric Topology Group Theory Primary: 57K43, Secondary: 20F65 A closed 4-manifold is symplectic Calabi--Yau (SCY) if its canonical class is trivial. Friedl and Vidussi proved that Thompson's group $F$ cannot be the fundamental group of any SCY manifold. In this paper, we show that its generalizations, called the Brown--Thompson group and the $n$-adic Lodha--Moore groups, cannot be also the fundamental group of any SCY manifold by using their method. From this proof, we also show that there exist non-trivial infinitely many examples which satisfy Geoghegan's conjecture. |
| title | The Lodha--Moore groups and their $n$-adic generalizations are not SCY |
| topic | Geometric Topology Group Theory Primary: 57K43, Secondary: 20F65 |
| url | https://arxiv.org/abs/2501.07522 |