All Questions

Consider the following 2-dimensional CW-complex: its 1-skeleton is $K_8$, which we write as an edge-disjoint union $K_5\cup K_{5,3}\cup K_3$. Then for any two edges $ab\in E(K_5)$ and $cd\in E(K_3)$ ...

A simplicial $d$-sphere is a simplicial complex homeomorphic to the $d$-sphere. It is known that not every such complex can be embedded into $\Bbb R^{d+1}$ as the boundary complex of a convex ...

Given a finite set $X \subset \mathbb{R}^n$, we can of course construct the corresponding Čech or Vietoris-Rips filtration. At each level of this filtration the scale parameter is fixed and unrelated ...

Consider a simplicial complex $C$. On its support $$|C|=\lbrace \alpha = \sum_{v\in C}\alpha_{v}v \mid 0\leq \alpha_{v} \leq 1 , \sum_{v\in C}\alpha_{v} =1\mbox{ and }v|{\alpha_{v}} \neq 0\mbox{ is a ...