On the topology of the moduli space of positive scalar curvature concordances
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910781658890240 |
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| author | Botvinnik, Boris Wraith, David J. |
| author_facet | Botvinnik, Boris Wraith, David J. |
| contents | Let $M$ be a manifold which admits a metric with positive scalar curvature (or a positive intermediate curvature in a suitable sense). We study the moduli space ${\mathscr{M}}^{\mathsf{pos}_*}_{\sqcup}(M\times I)_g$ of concordances of such metrics (with appropriate boundary conditions) which restrict to a given metric $g$ on $M \times \{0\} \cup\partial M \times I$. We show that $π_{4*}{\mathscr{M}}^{\mathsf{pos}_*}_{\sqcup}(M \times I)_g \otimes {\mathbb Q} \neq 0$ in a stable range provided $\dim M$ is even. We obtain analogous results when positive scalar curvature is replaced by $k$-positive Ricci curvature for $k \ge 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the topology of the moduli space of positive scalar curvature concordances Botvinnik, Boris Wraith, David J. Differential Geometry 53C20 Let $M$ be a manifold which admits a metric with positive scalar curvature (or a positive intermediate curvature in a suitable sense). We study the moduli space ${\mathscr{M}}^{\mathsf{pos}_*}_{\sqcup}(M\times I)_g$ of concordances of such metrics (with appropriate boundary conditions) which restrict to a given metric $g$ on $M \times \{0\} \cup\partial M \times I$. We show that $π_{4*}{\mathscr{M}}^{\mathsf{pos}_*}_{\sqcup}(M \times I)_g \otimes {\mathbb Q} \neq 0$ in a stable range provided $\dim M$ is even. We obtain analogous results when positive scalar curvature is replaced by $k$-positive Ricci curvature for $k \ge 2$. |
| title | On the topology of the moduli space of positive scalar curvature concordances |
| topic | Differential Geometry 53C20 |
| url | https://arxiv.org/abs/2407.21218 |