A remark on $Λ^2$-enlargeable manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917365242920960 |
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| author | Su, Guangxiang |
| author_facet | Su, Guangxiang |
| contents | In this note, we consider the case where the condition ``constant near infinity" in the definition of $Λ^2$-enlargeable manifolds is replaced by the condition ``locally constant near infinity" and prove that a $Λ^2$-enlargeable manifold in this modified sense still cannot carry a complete Riemannian metric of positive scalar curvature. As a consequence, we give another proof of Wang-Zhang's theorem on the generalized Geroch conjecture for complete spin manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark on $Λ^2$-enlargeable manifolds Su, Guangxiang Differential Geometry In this note, we consider the case where the condition ``constant near infinity" in the definition of $Λ^2$-enlargeable manifolds is replaced by the condition ``locally constant near infinity" and prove that a $Λ^2$-enlargeable manifold in this modified sense still cannot carry a complete Riemannian metric of positive scalar curvature. As a consequence, we give another proof of Wang-Zhang's theorem on the generalized Geroch conjecture for complete spin manifolds. |
| title | A remark on $Λ^2$-enlargeable manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.18329 |