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| The first steps -- Simplicial homology -- Beyond the simplicial setting -- Category of chain complexes -- Chain homotopy -- Connecting homomorphism -- Singular homology -- Cellular homology -- Simplicial collapses -- Organizing collapsing sequences -- Internal collapses and discrete Morse theory -- Explicit homology classes associated to critical cells -- The critical Morse complex -- Implications and variations -- Algebraic Morse theory -- Discrete Morse theory for posets -- Discrete Morse theory for CW complexes -- Discrete Morse theory and persistence. |
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