Relative H-Principle and Contact Geometry
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910868206256128 |
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| author | Taylor, Jacob |
| author_facet | Taylor, Jacob |
| contents | We show that if $F(M)$ is some space of holonomic solutions with space of formal solutions $F^f(M)$ that satisfies a certain relative $h$-principle, then the non-relative map $F(M) \to F^f(M)$ admits a section up to homotopy. We apply this to the relative $h$-principle for overtwisted contact structures proved by Borman-Eliashberg-Murphy to find infinite cyclic subgroups in the homotopy groups of the contactomorphism group of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_03185 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Relative H-Principle and Contact Geometry Taylor, Jacob Geometric Topology Algebraic Topology 53D35, 57R17, 58D99 We show that if $F(M)$ is some space of holonomic solutions with space of formal solutions $F^f(M)$ that satisfies a certain relative $h$-principle, then the non-relative map $F(M) \to F^f(M)$ admits a section up to homotopy. We apply this to the relative $h$-principle for overtwisted contact structures proved by Borman-Eliashberg-Murphy to find infinite cyclic subgroups in the homotopy groups of the contactomorphism group of $M$. |
| title | Relative H-Principle and Contact Geometry |
| topic | Geometric Topology Algebraic Topology 53D35, 57R17, 58D99 |
| url | https://arxiv.org/abs/2210.03185 |