6 problems

PL sphere-or-ball conjecture. If $[u,v]$ is full, then $(u,v)$ is a PL sphere of dimension $\rho(v)-\rho(u)-2$. Otherwise, $(u,v)$ is a PL ball of the same dimension.

Let $C$ be the specified 2-pentachoron cut-open Cappell--Shaneson complex, and let $B^4_C$ be the topological 4-ball containing $C$ described in the paper. Standardness conjecture…

Let $X$ be an Alexandrov space, meaning a finite-dimensional complete length space with curvature bounded below in the Alexandrov sense, and suppose that $X$ contains no proper ext…

Tame tangle manifolds are PL manifolds. The canonical PL structures of open or compact tame $m$-tangles restrict to PL $m$-manifold structures on tame tangle manifolds.

Let $s,d,r\ge2$ be integers satisfying … and let $K$ be a finite $s$-dimensional simplicial complex. An almost $r$-embedding is a map $f:K\to\mathbb R^d$ such that…

Let $D=D^{s_1}\sqcup\ldots\sqcup D^{s_r}$ be a disjoint union of $r$ disks, let $f:D\to B^d$ be a proper PL map such that…