Introduction to Applied Algebraic Topology: Persistent Homology

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Introduction Topology Applying Topology Examples What is Algebraic Topology? • Algebraic topology assigns algebraic invariants to topological spaces. • χ - Euler characteristic - Assigns integers to topological spaces - Homotopy Invariant Joshua Roberts Applied Algebraic Topology 5/ 42
Introduction Topology Applying Topology Examples What is Algebraic Topology? • Algebraic topology assigns algebraic invariants to topological spaces. • χ - Euler characteristic - Assigns integers to topological spaces - Homotopy Invariant • If X is homotopy equivalent to a polyhedron, χ(X) = #v − #e + #f Joshua Roberts Applied Algebraic Topology 5/ 42
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Introduction Topology Applying Topo
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Čech Complex Introduction Topology
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Rips Complex Introduction Topology
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Outline Introduction Topology Apply
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Introduction to Applied Algebraic Topology: Persistent Homology

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