L-spaces, taut foliations and fibered hyperbolic two-bridge links
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911572423606272 |
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| author | Santoro, Diego |
| author_facet | Santoro, Diego |
| contents | We prove that if $M$ is a rational homology sphere that is Dehn surgery on a fibered hyperbolic two-bridge link, then $M$ is not an $L$-space if and only if $M$ supports a coorientable taut foliation. As a corollary we show that if $K'$ is obtained by a non-trivial knot $K$ as result of an operation called two-bridge replacement, then all non-meridional surgeries on $K'$ support coorientable taut foliations. This operation generalises Whitehead doubling and as a particular case we deduce that all non-meridional surgeries on Whitehead doubles of a non-trivial knot support coorientable taut foliations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14914 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | L-spaces, taut foliations and fibered hyperbolic two-bridge links Santoro, Diego Geometric Topology We prove that if $M$ is a rational homology sphere that is Dehn surgery on a fibered hyperbolic two-bridge link, then $M$ is not an $L$-space if and only if $M$ supports a coorientable taut foliation. As a corollary we show that if $K'$ is obtained by a non-trivial knot $K$ as result of an operation called two-bridge replacement, then all non-meridional surgeries on $K'$ support coorientable taut foliations. This operation generalises Whitehead doubling and as a particular case we deduce that all non-meridional surgeries on Whitehead doubles of a non-trivial knot support coorientable taut foliations. |
| title | L-spaces, taut foliations and fibered hyperbolic two-bridge links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2304.14914 |