RSFT functors for strong cobordisms and applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912783671492608 |
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| author | Moreno, Agustin Zhou, Zhengyi |
| author_facet | Moreno, Agustin Zhou, Zhengyi |
| contents | We extend the hierarchy functors of [33] to the case of strong symplectic cobordisms, via deformations with Maurer--Cartan elements. In particular, we prove that the concave boundary of a strong cobordism has finite algebraic planar torsion if the convex boundary does, which yields a functorial proof of finite algebraic planar torsion for contact manifolds admitting strong cobordisms to overtwisted contact manifolds. We also show the existence of contact $3$-folds without strong cobordisms to the standard contact $3$-sphere, that are not cofillable. We also include generalizations of the theory relating our notion of algebraic planar torsion to Latschev--Wendl's notion of algebraic torsion, discussing variations from counting holomorphic curves with general constraints and invariants extracted from higher genera holomorphic curves from an algebraic perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00370 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | RSFT functors for strong cobordisms and applications Moreno, Agustin Zhou, Zhengyi Symplectic Geometry We extend the hierarchy functors of [33] to the case of strong symplectic cobordisms, via deformations with Maurer--Cartan elements. In particular, we prove that the concave boundary of a strong cobordism has finite algebraic planar torsion if the convex boundary does, which yields a functorial proof of finite algebraic planar torsion for contact manifolds admitting strong cobordisms to overtwisted contact manifolds. We also show the existence of contact $3$-folds without strong cobordisms to the standard contact $3$-sphere, that are not cofillable. We also include generalizations of the theory relating our notion of algebraic planar torsion to Latschev--Wendl's notion of algebraic torsion, discussing variations from counting holomorphic curves with general constraints and invariants extracted from higher genera holomorphic curves from an algebraic perspective. |
| title | RSFT functors for strong cobordisms and applications |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2308.00370 |