Introduction to Applied Algebraic Topology: Persistent Homology

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Introduction Topology Applying Topology Examples Simplicial Homology Simplicial Complex Homology • Given a simplicial complex X, Define the n th homology of X to be the quotient vector space H n (X) = “Cycles”/“Boundaries” Joshua Roberts Applied Algebraic Topology 14/ 42
Introduction Topology Applying Topology Examples Simplicial Homology Simplicial Complex Homology • Given a simplicial complex X, Define the n th homology of X to be the quotient vector space H n (X) = “Cycles”/“Boundaries” H 1 (X) = ([a + b + c] + [d + e + f ])/∂K Joshua Roberts Applied Algebraic Topology 14/ 42
Page 1 and 2: Introduction Topology Applying Topo
Page 27 and 28: Outline Introduction Topology Apply
Page 29 and 30: Simplices Introduction Topology App
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Page 35 and 36: Triangulations Introduction Topolog
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Page 45: Introduction Topology Applying Topo
Page 57 and 58: Betti Numbers Introduction Topology
Page 63 and 64: Point-Clouds Introduction Topology
Page 71 and 72: Čech Complex Introduction Topology
Page 77 and 78: Rips Complex Introduction Topology
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Introduction Topology Applying Topo
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Outline Introduction Topology Apply
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Introduction to Applied Algebraic Topology: Persistent Homology

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