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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2512.10107 |
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| _version_ | 1866909956378198016 |
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| author | Buckminster, Ellis Taylor, Samuel J. |
| author_facet | Buckminster, Ellis Taylor, Samuel J. |
| contents | Thurston introduced the notion of a universal circle associated to a taut foliation of a $3$-manifold as a way of organizing the ideal circle boundaries of its leaves into a single circle action. Calegari--Dunfield proved that every taut foliation of an atoroidal $3$-manifold $M$ has a universal circle, but the uniqueness (or lack-thereof) of this structure remains rather mysterious.
In this paper, we consider the foliations associated to an Anosov flow $φ$ on $M$, showing that several constructions of a universal circle in the literature are typically distinct. Moreover, the underlying action of the Calegari--Dunfield leftmost universal circle is generally not even conjugate to the universal circle arising from the boundary of the flow space of $φ$. Our primary tool is a way to use the flow space of $φ$ to parameterize the circle bundle at infinity of $φ$'s invariant foliations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal circles for Anosov foliations Buckminster, Ellis Taylor, Samuel J. Geometric Topology Thurston introduced the notion of a universal circle associated to a taut foliation of a $3$-manifold as a way of organizing the ideal circle boundaries of its leaves into a single circle action. Calegari--Dunfield proved that every taut foliation of an atoroidal $3$-manifold $M$ has a universal circle, but the uniqueness (or lack-thereof) of this structure remains rather mysterious. In this paper, we consider the foliations associated to an Anosov flow $φ$ on $M$, showing that several constructions of a universal circle in the literature are typically distinct. Moreover, the underlying action of the Calegari--Dunfield leftmost universal circle is generally not even conjugate to the universal circle arising from the boundary of the flow space of $φ$. Our primary tool is a way to use the flow space of $φ$ to parameterize the circle bundle at infinity of $φ$'s invariant foliations. |
| title | Universal circles for Anosov foliations |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2512.10107 |