If you generate points in $\mathbb R^n$ via a process that respects a Gaussian normal distribution, then compute the persistent homology / barcodes, to my eye something fairly regular seems to be ...
Suppose I have a group acting on some Hadamard manifold, and I want to understand as much as possible about the (co)homology of the quotient. In my case I can find a fundamental domain for the action ...
Haken's paper "Theorie der Normalflächen" is one of the formative papers in the development of normal surface theory and provides an algorithm for detecting the unknot. While there are now a variety ...