Title: Topological persistence in geometry and analysis /
Authors: Polterovich, Leonid, 1963-; Rosen, Daniel, 1980-; Samvelyan, Karina, 1988-; Zhang, Jun, 1988-
Year: 2020
Subjects: Algebraic topology; Homology theory; Combinatorial topology; Symplectic geometry; Mathematical analysis; Algebraic topology; Combinatorial topology; Homology theory; Mathematical analysis; Symplectic geometry; Algebraic topology -- Applied homological algebra and category theory [See also 18Gxx] -- None of the above, but in this section.; Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- Calculus on manifolds; nonlinear operators [See also 46Txx,; Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx].
Contents: Definition and first examples -- Barcodes -- Proof of the isometry theorem -- What can we read from a barcode? -- Applications of Rips complexes -- Topological function theory -- A concise introduction to symplectic geometry -- Hamiltonian persistence modules -- Symplectic persistence modules.