Extending persistence using Poincaré and Lefschetz duality
From MaRDI portal
Publication:1029553
DOI10.1007/s10208-008-9027-zzbMath1189.55002OpenAlexW4251358505WikidataQ59442786 ScholiaQ59442786MaRDI QIDQ1029553
David Cohen-Steiner, Herbert Edelsbrunner, John L. Harer
Publication date: 13 July 2009
Published in: Foundations of Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10208-008-9027-z
Symbolic computation and algebraic computation (68W30) Homology and cohomology theories in algebraic topology (55N99) PL-topology (57Q99)
Related Items (41)
Structure and stability of the one-dimensional Mapper ⋮ Topological graph persistence ⋮ Algebraic stability of zigzag persistence modules ⋮ Categorified Reeb graphs ⋮ A topological approach for protein classification ⋮ Topological persistence for circle-valued maps ⋮ Topology of angle valued maps, bar codes and Jordan blocks ⋮ Some equivalence relation between persistent homology and morphological dynamics ⋮ Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions ⋮ Metrics for generalized persistence modules ⋮ Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics ⋮ Stabilizing the unstable output of persistent homology computations ⋮ Reeb graphs: approximation and persistence ⋮ Revisiting graph persistence for updates and efficiency ⋮ Coreduction homology algorithm for inclusions and persistent homology ⋮ Topological Data Analysis of Single-Cell Hi-C Contact Maps ⋮ Zigzag persistence ⋮ Unnamed Item ⋮ Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis ⋮ Optimal topological simplification of discrete functions on surfaces ⋮ Persistent Intersection Homology for the Analysis of Discrete Data ⋮ Barcode embeddings for metric graphs ⋮ Probabilistic convergence and stability of random mapper graphs ⋮ Categorification of persistent homology ⋮ Statistical Analysis and Parameter Selection for Mapper ⋮ Parametrized homology via zigzag persistence ⋮ Lipschitz functions have \(L_{p}\)-stable persistence ⋮ Persistent intersection homology ⋮ A persistence landscapes toolbox for topological statistics ⋮ TRACKING A GENERATOR BY PERSISTENCE ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ Flow-complex-based shape reconstruction from 3D curves ⋮ Measuring and computing natural generators for homology groups ⋮ Local versus global distances for zigzag and multi-parameter persistence modules ⋮ SimBa ⋮ W-Structures in Contour Trees ⋮ Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes ⋮ Relative persistent homology ⋮ Correspondence modules and persistence sheaves: a unifying perspective on one-parameter persistent homology ⋮ Homological reconstruction and simplification in \(\mathbb{R}^3\) ⋮ Continuous and discrete radius functions on Voronoi tessellations and Delaunay mosaics
Uses Software
Cites Work
This page was built for publication: Extending persistence using Poincaré and Lefschetz duality