We study the computability degree of real numbers arising as L 2 -Betti or -torsion groups, parametrised over Turing word problem.

Analysis of multidimensional data is challenging. Topological invariants can be used to summarize essential features of such data sets. In this work, we propose to compute the Betti numbers from a generative model based on a simplicial complex learnt from the data. We compare it to the Witness Complex, a geometric technique based on nearest neighbors. Our results on different data distributions...

This paper presents statistical approaches to testing whether data are spherical in the topological sense, ie, they lie on a closed manifold with a hollow interior. We characterize the sphere by it’s Betti numbers and use the computational topology program PLEX [12] based on simplicial complexes to calculate the data’s Betti numbers. We use the parametric bootstrap approach to test the power of...