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2 votes
0 answers
109 views

Description of a point cloud being "undersampled" wrt persistent homology, confidence level?

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 ...
32 votes
4 answers
7k views

Computational software in Algebraic Topology?

I was wondering if there is any good software out there that allows you to do specific computations in algebraic topology. For example: Create a simplicial complex/set and ask questions about its ...
7 votes
1 answer
224 views

Computing homology of subvarieties of Euclidean spaces by persistent homology

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 ...
5 votes
2 answers
371 views

Is there an upper bound on the number of points in point cloud for which we compute the persistent homology?

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 ...
5 votes
1 answer
237 views

Triangulation of the surface determined by sampling two of its cross-sections

I have a data set that essentially looks like the picture below, i.e., it's given by sets of points in $\mathbb{R}^3$ that sample the cross-sections of a certain surface that in principle I do not ...