Abstract:We construct and study an $H$-space multiplication on ${\mathcal {R}}^+(M)$ for manifolds $M$ which are nullcobordant in their own tangential $2$-type. This is applied to give a rigidity criterion for the action of the diffeomorphism group on ${\mathcal {R}}^+(M)$ via pullback. We also compare this to other known multiplicative structures on ${\mathcal {R}}^+(M)$.

---

中文翻译：

---

𝐻-正标量曲率度量空间上的空间结构

摘要：我们构造并研究了 ${\mathcal {R}}^+(M)$ 上的 $H$-空间乘法，用于流形 $M$，它们在它们自己的切线 $2$ 类型中是空共边的。这用于通过回拉给出微分同胚群对 ${\mathcal {R}}^+(M)$ 的作用的刚性标准。我们还将其与 ${\mathcal {R}}^+(M)$ 上的其他已知乘法结构进行了比较。

---