Abstract:We generalize Milnor link invariants to surface-links in 4-space, possibly with boundary. To this end, we introduce the notion of cut-diagram, which is a 2-dimensional analogue of Gauss diagrams. To each cut-diagram, we associate a group extending the fundamental group of the exterior of a surface-link, and we extract Milnor-type invariants from its successive nilpotent quotients. We show that this yields concordance invariants for surface-links, and that some even are link-homotopy invariants. We give several concrete applications, including realization and classification results. The theory of cut-diagrams is further investigated, heading towards a combinatorial approach to surfaces in 4-space.
From: Jean-Baptiste Meilhan [view email]
[v1]
Wed, 29 Sep 2021 17:15:37 UTC (276 KB)
[v2]
Tue, 22 Nov 2022 07:33:53 UTC (285 KB)
[v3]
Tue, 7 Nov 2023 13:22:28 UTC (283 KB)
[v4]
Sat, 29 Nov 2025 10:20:14 UTC (298 KB)
[v5]
Thu, 18 Jun 2026 12:16:40 UTC (929 KB)
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