4 papers
Combinatorial link concordance using cut-diagrams
Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara
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…
Milnor-type invariants for surface-links and cut-diagrams
Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara
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…
A universal finite type invariant of knots in homology 3-spheres
Benjamin Audoux, Delphine Moussard
An essential goal in the study of finite type invariants of some objects (knots, manifolds) is the construction of a universal finite type invariant, universal in the sense that it…
Welded graphs, Wirtinger groups and knotted punctured spheres
Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara
We develop a general diagrammatic theory of welded graphs, and provide an extension of Satoh's Tube map from welded graphs to ribbon surface-links. As a topological application, we…