7 problems

Let $\mathcal{X}$ be a collection of topological spaces, and let $\prod\mathcal{X}$ denote the collection of spaces homotopy equivalent to a finite-type product of spaces in…

Let $K$ be a simplicial complex, and let $(\underline{X},\underline{A})^K$ denote the associated polyhedral product. Bahri, Bendersky, Cohen, and Gitler constructed an integral dec…

Let $K$ be a shifted complex or a flag complex with chordal $1$-skeleton. The decomposition in Theorem is a decomposition of loop spaces that should deloop. However, this does not…

Let $K$ be a simplicial complex on $[m]$, let $F$ be a compact subspace of ${\mathbb R}^n$, and let $c$ denote a single point. For a simplicial complex $K$, write $|K|$ for its geo…

BBCG desuspension conjecture. The result of Grbić and Theriault for $\mathcal{Z}_K(D^2,S^1)$ when $K$ is shifted should generalize to a desuspension of the BBCG decomposition.

Golod characterization. The moment-angle complex $(D^2,S^1)^K$ is a co-$H$-space if and only if $K$ is Golod.

Let $K$ be a shifted simplicial complex, let $(CX_i,X_i,x_i)$ be based pairs indexed by the vertices of $K$, and write $Z(K;(\underline{CX},\underline{X}))$ for the associated poly…