5 problems

Metric thickening finite-support homotopy equivalence conjecture. The inclusion induces a homotopy equivalence

Let $X$ be a metric space, potentially with additional assumptions, let $r\geq 0$, and let … Here $\operatorname{VR}^{\mathrm{m}}(X;r)$ denotes the metric Vietoris–Rips thickening…

Let $M=(X,K,\phi)$ be a simplicial metric thickening, with metric thickening $\mathcal{M}\subseteq\mathcal{P}(X)$. Let $\hat{M}$ be the closure of $\mathcal{M}$ in $\mathcal{P}(X)$…

Let $k\geq 1$, let $r$ satisfy … let $\mu\in\mathrm{VR}^m(S^1;r)$, and let $\iota$ map the boundary of the Barvinok–Novik orbitope $\mathcal{B}_{2k}$ into the Vietoris–Rips metric…

Let $S^1$ be the unit circle, let $r>0$, and let $\mathrm{VR}^m(S^1;r)$ denote its Vietoris–Rips metric thickening. For each integer $k\geq 1$, let $\mathcal{B}_{2k}$ be the Barvin…