Overview
We consider a generalization of this persistent homology called levelset zigzag persistent homology and make a survey about how the various linked mathematical frameworks relate to one another. We implement a web application that allows for a visualizing how levelset zigzag homology works when it is used to study the shape of spaces and point-cloud data.
Approach
For this work, we make use of the topology and geometry library GUDHI for the core algorithms. We use both PyVis and Plotly for everything related to visualisation purposes, and wrap a part of the project (the diagram bijection) as a Streamlit web app product.