3 problems

Let $G(T,\delta,m)$ be the preferential attachment graph and let its Rips complex of radius $r$ be formed using the graph metric. Diameter-dominance conjecture. The Betti numbers o…

Let $X$ be a finite subset of Euclidean space, let $\mathcal{R}(X)$ be its Rips complex, and let $\mathcal{S}(X)$ be its shadow complex. Let … be the projection. The all-dimensiona…

Let $X\subseteq\mathbb{R}^3$ be finite and let $v\in X$. Write $X_v$ for the subset associated with the vertex $v$, $X^v$ for the corresponding closed neighborhood, and $X-v$ for…