2 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…

Let $P$ and $N$ be manifolds of dimensions $p$ and $n$, respectively, and let $f\colon P\to N$ be an immersion equipped with a lift $f_{j-1}\in E_{j-1}(P,N)$. For $j\geq 2$, let…