Milnor-type invariants for surface-links and cut-diagrams

Benjamin Audoux; Jean-Baptiste Meilhan; Akira Yasuhara

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arXiv · 2109.14578

Milnor-type invariants for surface-links and cut-diagrams

Benjamin Audoux·Jean-Baptiste Meilhan·Akira Yasuhara

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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.

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Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara. 2021-09-29. Milnor-type invariants for surface-links and cut-diagrams. https://arxiv.org/abs/2109.14578

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