4 problems

Let $m$, $p$, and $n$ be integers, let $\mathcal{L}_{m\cdot p}^{n}$ be the space of long links with $m$ components of dimension $p$ in $\mathbb{R}^{n}$, and let…

Let $n$, $p$, and $m$ be integers with $m\geq 2$ and $1\leq p\leq n-3$. Let $\mathcal{L}_{m\cdot p}^{n}$ denote the space of long links with $m$ components of dimension $p$ in…

Let $\mathcal{K}^{m\bullet}_d$ be the cosimplicial space of long links of $m$ strands in $\mathbb{R}^d$ constructed by Munson and Volić, and let its homology Bousfield–Kan spectral…

Quasi-isomorphism conjecture. The cochain maps from Theorem 1 are quasi-isomorphisms for $n>3$. This conjecture asserts that the diagram complexes calculate the cohomology of space…