2 problems

Let $\Cwiggle=C_{U\kern-.5pt\left(p^{k}\right)}\left(\Delta_{k}\right)/\left(\Delta_{k}\times S^{1}\right)$, where $C_{U\left(p^k\right)}(\Delta_k)$ is the centralizer of…

Let $\Lcal_n$ be the partition complex, let $\Pcal_n^\diamond$ denote the unreduced suspension of the partition complex associated to the partition lattice, and let…