Non-negative scalar curvature on spin surgeries and Novikov conjecture
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914207392333824 |
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| author | Wang, Jinmin |
| author_facet | Wang, Jinmin |
| contents | Let $M$ be a closed aspherical manifold. Assume that the rational strong Novikov conjecture holds for $π_1(M)$. We show that on any spin surgery of $M$ along a region whose induced homomorphism on the fundamental group is trivial, every complete metric with non-negative scalar curvature is Ricci-flat. In particular, on the connected sum of $M$ with a spin manifold, any complete metric with non-negative scalar curvature is Ricci-flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-negative scalar curvature on spin surgeries and Novikov conjecture Wang, Jinmin Differential Geometry K-Theory and Homology Let $M$ be a closed aspherical manifold. Assume that the rational strong Novikov conjecture holds for $π_1(M)$. We show that on any spin surgery of $M$ along a region whose induced homomorphism on the fundamental group is trivial, every complete metric with non-negative scalar curvature is Ricci-flat. In particular, on the connected sum of $M$ with a spin manifold, any complete metric with non-negative scalar curvature is Ricci-flat. |
| title | Non-negative scalar curvature on spin surgeries and Novikov conjecture |
| topic | Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2512.16535 |