分野別セミナー

We introduce the double cohomology of a moment angle complex. Given a finite metric space S, which we can consider as a data set, we can take its Vietoris-Rips complex and then take its homology we get the persistent homology of S. This satisfies a stability property which roughly says that if we change S slightly, its persistent homology also only changes slightly. If instead we take the moment angle complex of Vietoris-Rips and then take homology, it turns out we lose the stability property. The double cohomology was introduced to solve this problem. It turns out that the double cohomology also seems to detect when a simplicial complex can be written as a nontrivial connected sum of two other simplicial complexes. The talk will give a gentle introduction to persistent homology, moment angle complexes and the double cohomology.

This is joint work with Tony Bahri, Ivan Limenchenko, Taras Panov and Jongbaek Song.