Introductory reading

This is a list of entries to the vastly growing literature in the field of topological data analysis, both from a theoretical and an applied point of view.

Literature for Mathematicians

A well-known theoretical introduction to the field. Carlsson: Topology and Data.

One of the papers introducing the notion of persistent homology of a filtration. Zomorodian and Carlsson: Computing persistent homology.

A recently introduced topological summary better suited than persistence diagrams to statistically analyze persistent homology, the persistence landscape. Bubenik: Statistical topological data analysis using persistence landscapes.

Literature for Computer Scientists

A thorough introduction to the field and approaches of computational topology. Edelsbrunner and Harer: Computational topology: an introduction.

A general overview of persistent homology with an eye towards applications of different numerical libraries. In the supplementaries starting points for own numerical steps are given. Otter et al: A roadmap for the computation of persistent homology.

The mapper algorithm. Singh et al: Topological methods for the analysis of high dimensional data sets and 3d object recognition.

Literature for Physicists

Starting with a topological primer, the computational setup is described and applied to immensely large structures present in our universe: the cosmic web. Pranav et al: The Topology of the Cosmic Web in Terms of Persistent Betti Numbers.