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Archaeology of persistence
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Classroom Contents
Ulrich Bauer - Persistence Diagrams as Diagrams
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- 1 Intro
- 2 Archaeology of persistence
- 3 The many faces of persistence
- 4 Inerval decompositions and persistence modules
- 5 Persistence and stability: the big picture
- 6 The category of matchings
- 7 From barcodes to matching diagrams (and back)
- 8 A category of barcodes
- 9 Bottleneck distance as an interleaving distance
- 10 Non-functorality of persistence barcodes
- 11 Structure of persistence sub quotient modules
- 12 Persistence sub-/quotient modules and their matching diagrams
- 13 Algebraic stability via induced matchings
- 14 The categorified induced matching theorem
- 15 A general criterion for trivial colkernels
- 16 The induced matching theorem for monos and epis
- 17 The algebraic stability theorem categorically
- 18 Barcodes from scratch
- 19 A rank formula for barcodes
