4 problems

Three-component connectivity conjecture. The map $l_3$ is $(3n-\max\{2p_1+p_2+p_3,p_1+2p_2+p_3,p_1+p_2+2p_3\}-5)$-connected.

Connectivity conjecture. The map $l_2$ is $(2n-\max\{2p+q,2q+p\}-3)$-connected.

Classification conjecture. There are bijections

Let $M$ be a manifold, let $\mathcal{O}^s_\infty(M)$ and $\widetilde{\mathcal{O}}^s_k(\mathbb{R}^m)$ be the source categories of the continuous context-free functors under consider…