Persistent algebraic topology and topological data analysis
Introductory
Carlsson, Persistent Homology and Applied Homotopy Theory, arXiv:2004.00738 [math.AT]
Huber, Persistent homology in data science
Edelsbrunner and Harrer, Persistent homology – a survey
Zomorodian and Carlsson, Computing persistent homology
Comprehensive
Oudot, Persistence Theory: From Quiver Representations to Data Analysis
Edelsbrunner and Harrer, Computational topology: an introduction
Persistent homotopy
Jardine, Persistent homotopy theory
Some applications to physics
M. Biagetti, A. Cole, G. Shiu, The Persistence of Large Scale Structures I: Primordial non-Gaussianity, JCAP 04 (2021) 061
A. Cole, M. Biagetti, G. Shiu, Topological Echoes of Primordial Physics in the Universe at Large Scales, arXiv:2012.03616 [astro-ph.CO]
J. H. T. Yip et al, Cosmology with Persistent Homology: a Fisher Forecast, JCAP 09 (2024) 034.