Stein-fillability and positivity in the mapping class group
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915378356027392 |
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| author | Brejevs, Vitalijs Wand, Andy |
| author_facet | Brejevs, Vitalijs Wand, Andy |
| contents | We construct an infinite family of non-positive open books with once-punctured torus pages that support Stein-fillable contact structures. Combined with a result of Wendl, this allows us to give a complete answer to a long-standing question about the mapping class group of a compact surface with boundary: namely, we conclude that the monoid of monodromies supporting Stein-fillable contact structures is equal to the monoid of positive monodromies if and only if the surface is planar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07707 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stein-fillability and positivity in the mapping class group Brejevs, Vitalijs Wand, Andy Geometric Topology Symplectic Geometry 57R17, 53D10 We construct an infinite family of non-positive open books with once-punctured torus pages that support Stein-fillable contact structures. Combined with a result of Wendl, this allows us to give a complete answer to a long-standing question about the mapping class group of a compact surface with boundary: namely, we conclude that the monoid of monodromies supporting Stein-fillable contact structures is equal to the monoid of positive monodromies if and only if the surface is planar. |
| title | Stein-fillability and positivity in the mapping class group |
| topic | Geometric Topology Symplectic Geometry 57R17, 53D10 |
| url | https://arxiv.org/abs/2405.07707 |