Nonperiodic leaves of codimension one foliations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913833074819072 |
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| author | Cotón, Carlos Meniño |
| author_facet | Cotón, Carlos Meniño |
| contents | In this work we exhibit examples of $5$-manifolds that are not homeomorphic to any leaf of any $C^2$ codimension one foliation of any compact $6$-manifold but are homeomorphic to (proper) leaves of some $C^1$ codimension one foliations and also to (proper) leaves of some $C^\inf$ codimension $2$ foliations. As far as we know, this is the first example of this nature. In addition, it is shown examples of $C^{r}$ codimension one foliations, $r\in[0,2)$, with a minimal invariant set whose leaves are pairwise nonhomeomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10485 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonperiodic leaves of codimension one foliations Cotón, Carlos Meniño Geometric Topology 37C86, 57R30 In this work we exhibit examples of $5$-manifolds that are not homeomorphic to any leaf of any $C^2$ codimension one foliation of any compact $6$-manifold but are homeomorphic to (proper) leaves of some $C^1$ codimension one foliations and also to (proper) leaves of some $C^\inf$ codimension $2$ foliations. As far as we know, this is the first example of this nature. In addition, it is shown examples of $C^{r}$ codimension one foliations, $r\in[0,2)$, with a minimal invariant set whose leaves are pairwise nonhomeomorphic. |
| title | Nonperiodic leaves of codimension one foliations |
| topic | Geometric Topology 37C86, 57R30 |
| url | https://arxiv.org/abs/2404.10485 |