2 problems

Loop-space conjecture. The space $\operatorname{\mathcal{R}^\text{Cores}}(\operatorname{S}^n)$ equipped with $\mu$ is an associative $H$-space and is homotopy equivalent to a loop…

Let $W^8$ be the unit sphere bundle of the unique nontrivial vector bundle of rank $7$ over $S^2$, and let $\mathbb{C}\mathbb{P}^2 \times \mathbb{C}\mathbb{P}^2$ be the product of…