2021/09/29 by Benjamin Audoux, Audoux, Benjamin, Jean–Baptiste Meilhan +3
Mathematics · #57K12 #57K45 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2109.14578
openalex publication_date 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.