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Algebraic Topology
The newest papers in Algebraic Topology that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
17 papers, from 7 September 2026 to 4 November 2026: 17 arXiv preprints.
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Newest papers
ToroFit: Fitting Wedge Sums of Tori to High-Dimensional Data
Data arising in scientific applications often exhibits complex nonlinear structure.Multipartite Entanglement, TQFT Partition Functions and PL Bordism
In a previous work we conjectured that the multi-invariants of the ground state of a gapped $(d-1)+1$-dimensional system, labeled by bipartite $(d+1)$-edge-colored graphs encoding closed oriented…The geometry of Floquet states
This paper studies the moduli space of "good" periodic Hamiltonians, i.e., periodic Hamiltonians with nondegenerate Floquet spectrum.Exact Topological Compliance: Generating Persistence-Equivalent Graphs
Persistent homology summarizes the topological evolution of a graph as persistence diagrams (PDs).Constructive Bounds for the Topological Expressivity of Neural Networks
The expressivity of a neural network $Φ$ describes the class of functions that a network can express.Cups and Gates II: Operads, twists, and addressable intra-code gates
In Part I, we introduced a general framework for constructing logical gates in quantum CSS codes from cohomology invariants, focusing on cup products and their generalizations from topological to…The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
Multiparameter persistent homology is a rapidly developing branch of topological data analysis that improves the robustness of single-parameter persistent homology to outliers, while still capturing…A Complete Proof of $\mathsf{QMA}_1$-Hardness for Weighted Gapped Clique Homology
The computational complexity of simplicial homology has been studied since the question was raised by Kaibel and Pfetsch, and clique homology was later shown to be $\mathsf{QMA}_1$-hard by Crichigno…A differentiability framework for zigzag persistent homology via linear interpolation
Persistent homology can be differentiated and incorporated into learning pipelines, but no analogous framework exists for zigzag persistence, which is needed when the underlying topological…T-ARC: Topology-Aware Randomized Clustering via Distributionally Robust Stochastic Block Models
In this work, we introduce a new clustering method, namely T-ARC (Topology-Aware Randomized Clustering), that corrects the geometric bias of K-means by embedding topological information directly…A data structure for quotient flag complexes
Vietoris-Rips filtrations, which are standard in topological data analysis, are flag complexes, and a simplex tree stores these without any attaching data.LandscapeSHAP: Which Persistent Homology Class Gets the Credit?
Shapley values, a solution concept from cooperative game theory, have recently become a standard tool for feature credit allocation in machine learning.What Converges in the Platonic Representation Hypothesis? Structure over Geometry
The Platonic Representation Hypothesis suggests that increasingly capable models converge toward shared representations.Homological Trimming and Regularity of Filtrations via Local Obstruction Modules
Existing link-based combinatorial preprocessing methods speed up the computation of persistent homology by removing a vertex or edge only when its link remains a cone.COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules
Every multiparameter persistence vectorization we know of carries a one-sided Lipschitz upper bound and nothing below it: without a lower gauge there is no sense in which the features are faithful…Certified Topological Interaction in Neural Representations: Class Disentanglement Is Mostly Pairwise
Class disentanglement (the separation of a representation's class-conditional point clouds along depth and over training) is usually read off descriptive curves.CodeTD: Topology of Attention Detects Hallucinations in Code LLMs
As AI-code assistant tools become widespread, automatic assessment of the correctness of generated code becomes a significant challenge.