4 problems

Let $M$ be a smooth closed manifold of dimension $n$, and let $F_2(M)$ denote its ordered configuration space of two distinct points. The unordered configuration space is…

Boundary-generic realization conjecture. The constraints

Projective h-principle fundamental-group conjecture. If $X$ is a complex projective manifold satisfying the $h$-principle, then $\pi_1(X)$ is almost abelian.

The h-principle fundamental-group conjecture. Every projective manifold satisfying the $h$-principle should have an almost abelian fundamental group.