2 problems

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…