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Combinatorial link concordance using cut-diagrams
[Submitted on 27 Mar 2026 (v1), last revised 18 Jun 2026 (this v · 2026-06-19 · via math updates on arXiv.org

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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.

Submission history

From: Jean-Baptiste Meilhan [view email]
[v1] Fri, 27 Mar 2026 12:47:29 UTC (143 KB)
[v2] Thu, 18 Jun 2026 13:38:19 UTC (143 KB)