Moduli spaces of Ricci positive metrics in dimension five
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910453201895424 |
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| author | Goodman, McFeely Jackson |
| author_facet | Goodman, McFeely Jackson |
| contents | We use the $η$ invariants of spin$^c$ Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many non-diffeomorphic five dimensional manifolds for which these moduli spaces each have infinitely many components. The manifolds are total spaces of principal $S^1$ bundles over $\#^a\mathbb{C}P^2\#^b\overline{\mathbb{C}P^2}$ and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify 5-manifolds with fundamental group $\mathbb{Z}_2$ admitting free $S^1$ actions with simply connected quotients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_00333 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Moduli spaces of Ricci positive metrics in dimension five Goodman, McFeely Jackson Differential Geometry 53C20 We use the $η$ invariants of spin$^c$ Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many non-diffeomorphic five dimensional manifolds for which these moduli spaces each have infinitely many components. The manifolds are total spaces of principal $S^1$ bundles over $\#^a\mathbb{C}P^2\#^b\overline{\mathbb{C}P^2}$ and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify 5-manifolds with fundamental group $\mathbb{Z}_2$ admitting free $S^1$ actions with simply connected quotients. |
| title | Moduli spaces of Ricci positive metrics in dimension five |
| topic | Differential Geometry 53C20 |
| url | https://arxiv.org/abs/2002.00333 |