TDA Materials

Class Lectures

• Zach: The Finite Simplicial Approximation Theorem
• Michael: TDA_Simplicial_Approximation_Theorem with notes
• Sai: SmithNormalForm
• Darren: TDA_Reading_Class___Complexes  
  • Björner, Topological Methods: http://publish.illinois.edu/ymb/files/2020/03/Bjorner_TopMeth.pdf 
  • Attali et. al, Vietoris–Rips complexes also provide topologically correct reconstructions of sampled shapes: https://www.sciencedirect.com/science/article/pii/S0925772112001423
  • Walker, Homotopy Type and Euler Characteristic of Partially Ordered Sets: https://www.sciencedirect.com/science/article/pii/S0195669881800455
• Wanchen: Singular Homology
• Zach: Persistence Modules
• Michael: TDA_Persistence_Landscapes

Books:

• Munkres: https://people.dm.unipi.it/benedett/MUNKRES-ETA.pdf
• Ghrist: https://www2.math.upenn.edu/~ghrist/notes.html
• Edelbrunner and Harer: https://www.maths.ed.ac.uk/~v1ranick/papers/edelcomp.pdf

TDA Survey Articles

• Chazal and Michel:  https://www.frontiersin.org/articles/10.3389/frai.2021.667963/full#B21
• Ghrist: https://www2.math.upenn.edu/~ghrist/preprints/HAD.pdf
• Ghrist: https://www2.math.upenn.edu/~ghrist/preprints/barcodes.pdf
• Carlsson: https://www.ams.org/journals/bull/2009-46-02/S0273-0979-09-01249-X/S0273-0979-09-01249-X.pdf

Introduction to Category Theory

• Leinster: https://arxiv.org/abs/1612.09375
• Spivak: https://arxiv.org/abs/1302.6946

This is a more advanced book, but it has a very good introduction to TDA

• Polterovich, Rosen, Samvelyan, Zhang: https://arxiv.org/abs/1904.04044