Cover Image

The Generalized Rank Invariant: Möbius invertibility, Discriminating Power, and Connection to Other Invariants

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Clause, Nathaniel, Kim, Woojin, Mémoli, Facundo
Format:	Preprint
Published:	2022
Subjects:	Algebraic Topology Computational Geometry 5N31, 55U99
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Ephemeral persistence features and the stability of filtered chain complexes
by: Mémoli, Facundo, et al.
Published: (2022)

Barcoding Invariants and Their Equivalent Discriminating Power
by: Escolar, Emerson G., et al.
Published: (2024)

The Persistent Topology of Optimal Transport Based Metric Thickenings
by: Adams, Henry, et al.
Published: (2021)

Super-Polynomial Growth of the Generalized Persistence Diagram
by: Kim, Donghan, et al.
Published: (2024)

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent
by: Carrière, Mathieu, et al.
Published: (2024)

An axiomatic treatment of Persistent Homology
by: Ura, Sergio Tsuyoshi, et al.
Published: (2024)

Approximate and discrete Euclidean vector bundles
by: Scoccola, Luis, et al.
Published: (2021)

Algebraic Wasserstein distances and stable homological invariants of data
by: Agerberg, Jens, et al.
Published: (2023)

Persistence and Topological Complexity
by: Mémoli, Facundo, et al.
Published: (2025)

The G-Gromov-Hausdorff Distance and Equivariant Topology
by: Lim, Sunhyuk, et al.
Published: (2025)

Distributed Persistent Homology for 2D Alpha Complexes
by: Jensen, Freya, et al.
Published: (2024)

Dowker's theorem for higher-order relations
by: de Silva, Vin, et al.
Published: (2025)

Monoidal Rips: Stable Multiparameter Filtrations of Directed Networks
by: Blaser, Nello, et al.
Published: (2025)

Lifting Cocycles: From Heuristic to Theory
by: Gaukstad, Sigurd, et al.
Published: (2025)

Contractibility of Vietoris-Rips Complexes of dense subsets in $(\mathbb{R}^n, \ell_1)$ via hyperconvex embeddings
by: Wang, Qingsong
Published: (2024)

Combinatorial Topological Models for Phylogenetic Networks and the Mergegram Invariant
by: Dłotko, Paweł, et al.
Published: (2023)

Estimating the persistent homology of $\mathbb{R}^n$-valued functions using function-geometric multifiltrations
by: André, Ethan, et al.
Published: (2024)

A notion of homotopy for directed graphs and their flag complexes
by: Chaplin, Thomas, et al.
Published: (2024)

Vietoris-Rips Complexes of Split-Decomposable Spaces
by: Gómez, Mario
Published: (2024)

Function-Rips complexes in persistent homotopy theory: Local stability and Latschev theorems
by: Oudot, Steve, et al.
Published: (2026)

It's All About Covers: Persistent Homology of Cover Refinements
by: Leitão, António
Published: (2026)

Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
by: Adams, Henry, et al.
Published: (2022)

The Walk-Length Filtration for Persistent Homology on Weighted Directed Graphs
by: Muñoz, David E., et al.
Published: (2025)

Critical edges in Rips complexes and persistence
by: Goričan, Peter, et al.
Published: (2023)

Discrete Microlocal Morse Theory
by: Brown, Adam, et al.
Published: (2022)

Morse theory of Euclidean distance functions from algebraic hypersurfaces
by: Guidolin, Andrea, et al.
Published: (2024)

Connected power operations and simplicial Poincaré duality
by: Cantero-Morán, Federico, et al.
Published: (2024)

Homotopical recognition of diagram categories
by: Chorny, Boris, et al.
Published: (2024)

Lifespan Functors and Natural Dualities in Persistent Homology
by: Bauer, Ulrich, et al.
Published: (2020)

Short, new proofs of Dowker duality
by: Yoon, Iris H. R.
Published: (2024)

Computing Connection Matrices of Conley Complexes via Algebraic Morse Theory
by: Torras-Casas, Álvaro, et al.
Published: (2025)

Persistent homology detects curvature
by: Bubenik, Peter, et al.
Published: (2019)

Morse theory for chromatic Delaunay triangulations
by: Natarajan, Abhinav, et al.
Published: (2024)

Persistence K-theory
by: Biran, Paul, et al.
Published: (2023)

Persistent Homology via Finite Topological Spaces
by: Kayacan, Selçuk
Published: (2025)

Topological Machine Learning with Unreduced Persistence Diagrams
by: Abreu, Nicole, et al.
Published: (2025)

Cubical Approximation for Directed Topology II
by: Krishnan, Sanjeevi
Published: (2023)

Minimal projective resolution and magnitude homology of geodetic metric spaces
by: Asao, Yasuhiko, et al.
Published: (2024)

Tensor Computation of Euler Characteristic Functions and Transforms
by: Cisewski-Kehe, Jessi, et al.
Published: (2025)

Stability of 0-dimensional persistent homology in enriched and sparsified point clouds
by: Lazovskis, Jānis, et al.
Published: (2025)