Abstract Persistent homology is a mathematical tool from topological data analysis. It performs multi-scale analysis on a set of points and identi?es clusters, holes, and voids therein. These latter topological structures complement standard feature representations, making persistent homology an attractive feature extractor for arti?cial intelligence. Research on persistent homology for AI is in its infancy, and is currently hindered by two issues: the lack of an accessible introduction to AI researchers, and the paucity of applications. In response, the ?rst part of this paper presents a tutorial on persistent homology speci?cally aimed at a broader audience without sacri?cing mathematical rigor. The second part contains one of the ?rst applications of persistent homology to natural language processing. Speci?cally, our Similarity Filtration with Time Skeleton (SIFTS) algorithm identi?es holes that can be interpreted as semantic “tie-backs” in a text document, providing a new document structure representation. We illustrate our algorithm on documents ranging from nursery rhymes to novels, and on a corpus with child and adolescent writings.