论文标题
RICCI阳性指标的模量空间五
Moduli spaces of Ricci positive metrics in dimension five
论文作者
论文摘要
我们使用自旋$^c $ dirac运算符的$η$不变式来区分带有正质曲率的Riemannian指标的Moduli空间的连接组件。然后，我们发现许多非形态的五个维歧管，这些模量空间都具有无限的许多组件。这些歧管是$ \＃^a \ Mathbb {c} p^2 \＃^b \ edimine {\ Mathbb {c} p^2} $上的总空间，$ \＃^a \ Mathbb {c} p^2 \＃^b \ edine overline {\ Mathbb {c} p^2} $。一路上，我们将5个manifolds与基本组$ \ mathbb {z} _2 $允许免费$ s^1 $动作分类。
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.
