论文标题
非弯曲指标的模量空间在$ s^2 \ times s^3 $的商标上
The moduli Space of nonnegatively curved metrics on quotients of $S^2\times S^3$ by involutions
论文作者
论文摘要
We show that for an orientable non-spin manifold with fundamental group $\mathbb{Z}_2$ and universal cover $S^2\times S^3,$ the moduli space of metrics of nonnegative sectional curvature has infinitely many path components.组件的代表是$ s^3 \ times s^3 $上的标准度量标准的商，或者是先前使用共纪剂构建的Brieskorn品种上的指标。使用Lefschetz固定点定理计算出的Spin $^C $ DIRAC运算符的相对$η$不变的组件。
We show that for an orientable non-spin manifold with fundamental group $\mathbb{Z}_2$ and universal cover $S^2\times S^3,$ the moduli space of metrics of nonnegative sectional curvature has infinitely many path components. The representatives of the components are quotients of the standard metric on $S^3\times S^3$ or metrics on Brieskorn varieties previously constructed using cohomogeneity one actions. The components are distinguished using the relative $η$ invariant of the spin$^c$ Dirac operator computed by means of a Lefschetz fixed point theorem.
