3 problems

Gálvez–Kock–Tonks conjecture. For any decomposition space $X$,

Let $G$ be a u.s.c. decomposition of $E^n$, let $H_G$ be the set of nondegenerate elements of $G$, and let $N_G$ denote the set used in the decomposition-space formulation. For eac…

Universality conjecture. $U$ is universal for complete decomposition spaces and cULF maps, in the sense that complete decomposition spaces are classified by cULF maps into $U$.