论文标题
在球体束及其商的球体束上的非负分段或阳性RICCI曲率指标的模量空间
Moduli space of non-negative sectional or positive Ricci curvature metrics on sphere bundles over spheres and their quotients
论文作者
论文摘要
我们表明，在$ s^7 $划分的所有总空间上，$ s^8 $（合理同源球）的所有总空间上的模量空间在所有路径上都具有无限的许多路径组件。此外，我们通过一定的意义进行了米尔诺球体商的差异分类，并表明非负分段的指标空间无限地具有许多路径成分。最后，通过相同类型的相互作用获得了Shimada Spheres的商的差异性有限性结果，我们表明，对于无限的歧管家族可以表达的类型，正ricci曲率指标的模量空间无疑是许多路径成分。
We show that the moduli space of positive Ricci curvature metrics on all the total spaces of $S^7$-bundles over $S^8$ which are rational homology spheres has infinitely many path components. Furthermore, we carry out the diffeomorphism classification of quotients of Milnor spheres by a certain involution and show that the moduli space of metrics of non-negative sectional on them has infinitely many path components. Finally, a diffeomorphism finiteness result is obtained on quotients of Shimada spheres by the same type of involution and we show that for the types that can be expressed by an infinite family of manifolds, the moduli space of positive Ricci curvature metrics has infinitely many path components.
