Topological persistence for circle-valued maps

DOI10.1007/s00454-013-9497-xzbMath1275.55009arXiv1104.5646OpenAlexW2156845097WikidataQ59442789 ScholiaQ59442789MaRDI QIDQ2391833

Dan Burghelea, Tamal Krishna Dey

Publication date: 5 August 2013

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.5646

zbMATH Keywords

topological persistencebar codeJordan cellpersistence for circle-valued maps

Mathematics Subject Classification ID

Topological manifolds (57N99) Fiber spaces and bundles in algebraic topology (55R99)

Related Items (15)

Categorified Reeb graphs ⋮ Discrete Morse theory for computing cellular sheaf cohomology ⋮ Topology of angle valued maps, bar codes and Jordan blocks ⋮ A refinement of Betti numbers and homology in the presence of a continuous function. I ⋮ A refinement of Betti numbers and homology in the presence of a continuous function, II: The case of an angle-valued map ⋮ Decomposition of pointwise finite-dimensional 𝕊1 persistence modules ⋮ Metrics for generalized persistence modules ⋮ Harder-Narasimhan filtrations and zigzag persistence ⋮ Refinement of Novikov-Betti numbers and of Novikov homology provided by an angle valued map ⋮ Alternative to Morse-Novikov theory for a closed 1-form. I ⋮ Book review of: D. Burghelea, New topological invariants for real- and angle-valued maps. An alternative to Morse-Novikov theory ⋮ Parametrized homology via zigzag persistence ⋮ Persistent local systems ⋮ A functorial Dowker theorem and persistent homology of asymmetric networks ⋮ SimBa

Cites Work

• Statistical ranking and combinatorial Hodge theory
• Stability of persistence diagrams
• Matrix multiplication via arithmetic progressions
• Extending persistence using Poincaré and Lefschetz duality
• Topology of angle valued maps, bar codes and Jordan blocks
• Computing persistent homology
• Topological persistence and simplification
• Stability of critical points with interval persistence
• Unzerlegbare Darstellungen. I. (Indecomposable representations. I)
• Persistent cohomology and circular coordinates
• Zigzag persistent homology and real-valued functions
• Zigzag persistent homology in matrix multiplication time
• Dynamics, Laplace transform and spectral geometry
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