Work

Combinatorial link concordance using cut-diagrams

Year: 2026

Type: preprint

Abstract: Cut-diagrams are diagrammatic objects, defined in dimensions 1 and 2, that generalize links in 3-space and surface-links in 4-space; in dimension 1, this coincides with the theory of welded links. Using cut-diagrams, we introduce an equivalence relation called cut-concordance, which encompasses the topological notion of concordance for classical links. Our main result is that the nilpotent peripheral system of 1-dimensional cut-diagrams is an invariant of cut-concordance, giving along the way a combinatorial version of a theorem of Stallings. We also investigate the relationship with several other equivalence relations in diagrammatic knot theory, in particular in connection with link-homotopy.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2603.26366

Authors: Audoux, Benjamin, Meilhan, Jean-Baptiste, Yasuhara, Akira

Institutions: Centre National de la Recherche Scientifique, Institut Fourier, Université Grenoble Alpes, Waseda University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7143475670

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