Moduli spaces of Ricci positive metrics in dimension five

Goodman, McFeely Jackson¹

¹ Department of Mathematics, Colby College, Waterville, ME, United States

Geometry & topology, Tome 28 (2024) no. 3, pp. 1065-1098.

Résumé

We use the $\eta$ invariants of ${\mathrm{spin}}^c$ Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many nondiffeomorphic five-dimensional manifolds for which these moduli spaces each have infinitely many components. The manifolds are total spaces of principal $S^1$ bundles over ${\#}^aℂP^2{\#}^b\overline{ℂP^2}$ 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.

Détail

DOI : 10.2140/gt.2024.28.1065

Keywords: moduli spaces, positive Ricci curvature

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