Relative aspherical conjecture and higher codimensional obstruction to positive scalar curvature
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910383913041920 |
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| author | He, Shihang |
| author_facet | He, Shihang |
| contents | Motivated by the solution of the aspherical conjecture up to dimension 5 [CL20][Gro20], we want to study a relative version of the aspherical conjecture. We present a natural condition generalizing the model $X\times\mathbb{T}^k$ to the relative aspherical setting. Such model is closely related to submanifold obstruction of positive scalar curvature (PSC), and would be in similar spirit as [HPS15][CRZ23] in codim 2 case. In codim 3 and 4, we prove results on how 3-manifold obstructs the existence of PSC under our relative aspherical condition, the proof of which relies on a newly introduced geometric quantity called the it spherical width. This could be regarded as a relative version extension of the aspherical conjecture up to dim 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative aspherical conjecture and higher codimensional obstruction to positive scalar curvature He, Shihang Differential Geometry Geometric Topology Motivated by the solution of the aspherical conjecture up to dimension 5 [CL20][Gro20], we want to study a relative version of the aspherical conjecture. We present a natural condition generalizing the model $X\times\mathbb{T}^k$ to the relative aspherical setting. Such model is closely related to submanifold obstruction of positive scalar curvature (PSC), and would be in similar spirit as [HPS15][CRZ23] in codim 2 case. In codim 3 and 4, we prove results on how 3-manifold obstructs the existence of PSC under our relative aspherical condition, the proof of which relies on a newly introduced geometric quantity called the it spherical width. This could be regarded as a relative version extension of the aspherical conjecture up to dim 5. |
| title | Relative aspherical conjecture and higher codimensional obstruction to positive scalar curvature |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2403.11957 |