A criterion for virtual Euler class one
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909394487214080 |
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| author | Liu, Yi |
| author_facet | Liu, Yi |
| contents | Let $M$ be an oriented closed hyperbolic $3$--manifold. Suppose that $w$ is a rational second cohomology class of $M$ with dual Thurston norm $1$. Upon the existence of certain nonvanishing Alexander polynomials, the author shows that the pullback of $w$ to some finite cover of $M$ is the real Euler class of some transversely oriented taut foliation on that cover. As application, the author constructs examples with first Betti number either $2$ or $3$, and partial examples with any first Betti number at least $4$, supporting Yazdi's virtual Euler class one conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11492 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A criterion for virtual Euler class one Liu, Yi Geometric Topology Primary 57R30, Secondary 57R20, 57K31 Let $M$ be an oriented closed hyperbolic $3$--manifold. Suppose that $w$ is a rational second cohomology class of $M$ with dual Thurston norm $1$. Upon the existence of certain nonvanishing Alexander polynomials, the author shows that the pullback of $w$ to some finite cover of $M$ is the real Euler class of some transversely oriented taut foliation on that cover. As application, the author constructs examples with first Betti number either $2$ or $3$, and partial examples with any first Betti number at least $4$, supporting Yazdi's virtual Euler class one conjecture. |
| title | A criterion for virtual Euler class one |
| topic | Geometric Topology Primary 57R30, Secondary 57R20, 57K31 |
| url | https://arxiv.org/abs/2411.11492 |