All Questions

I am completely new to topological data analysis, so I apologise if this is a well-known area of persistent homology, as well as for any imprecise language. Suppose we know completely the topological ...

Let $S$ be a simplicial complex and let $Bary(S)$ denote its barycentric subdivision. Of course, the geometric realizations of $S$ and $Bary(S)$ are homeomorphic. However, one issue that arises in ...

Let $M$ be a submanifold of the Euclidean space $\mathbb{R}^n$. Let $G$ be a finite group acting on $M$ freely. I want to compute the homology (or even the cohomology ring) of $M/G$. Suppose the ...

I am interested in the topic of persistent homology (topological data analysis). According to what I read, there is some roadblock in the analysis of "big data" using persistent homology as it is ...