On the Euler class one conjecture for fillable contact structures
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915254333603840 |
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| author | Liu, Yi |
| author_facet | Liu, Yi |
| contents | In this paper, it is proved that every oriented closed hyperbolic $3$--manifold $N$ admits some finite cover $M$ with the following property. There exists some even lattice point $w$ on the boundary of the dual Thurston norm unit ball of $M$, such that $w$ is not the real Euler class of any weakly symplectically fillable contact structure on $M$. In particular, $w$ is not the real Euler class of any transversely oriented, taut foliation on $M$. This supplies new counter-examples to Thurston's Euler class one conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14504 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Euler class one conjecture for fillable contact structures Liu, Yi Geometric Topology Primary 57K32, 57K18, Secondary 57K33 In this paper, it is proved that every oriented closed hyperbolic $3$--manifold $N$ admits some finite cover $M$ with the following property. There exists some even lattice point $w$ on the boundary of the dual Thurston norm unit ball of $M$, such that $w$ is not the real Euler class of any weakly symplectically fillable contact structure on $M$. In particular, $w$ is not the real Euler class of any transversely oriented, taut foliation on $M$. This supplies new counter-examples to Thurston's Euler class one conjecture. |
| title | On the Euler class one conjecture for fillable contact structures |
| topic | Geometric Topology Primary 57K32, 57K18, Secondary 57K33 |
| url | https://arxiv.org/abs/2409.14504 |