34 citations · 88 across the 17 of their papers we have counts for
17 papers · 1 filter
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…
Higher order Kirk invariants of link maps
Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara
We define numerical link-homotopy invariants of link maps of any number of components, which naturally generalize the Kirk invariant. The Kirk invariant is a link-homotopy invarian…
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…
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…
k-reduced groups and Milnor invariants
Benjamin Audoux, Jean-Baptiste Meilhan, Akira Yasuhara
We characterize, in an algebraic and in a diagrammatic way, Milnor string link invariants indexed by sequences where any index appears at most times, for any fixed . Th…
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…
Characterization of the reduced peripheral system of links
Benjamin Audoux, Jean-Baptiste Meilhan
The reduced peripheral system was introduced by Milnor in the fifties for the study of links up to link-homotopy, i.e. up to isotopies and crossing changes within each link compone…
Toward universality in degree 2 of the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant
Benjamin Audoux, Delphine Moussard
In the setting of finite type invariants for null-homologous knots in rational homology 3-spheres with respect to null Lagrangian-preserving surgeries, there are two candidates to…
On codimension two embeddings up to link-homotopy
Benjamin Audoux, Jean-Baptiste Meilhan, Emmanuel Wagner
We consider knotted annuli in 4-space, called 2-string-links, which are knotted surfaces in codimension two that are naturally related, via closure operations, to both 2-links and…
On hyperbolic knots in S^3 with exceptional surgeries at maximal distance
Benjamin Audoux, Ana G. Lecuona, Fionntan Roukema
Baker showed that 10 of the 12 classes of Berge knots are obtained by surgery on the minimally twisted 5-chain link. In this article we enumerate all hyperbolic knots in S^3 obtain…
Extensions of some classical local moves on knot diagrams
Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan +1
In the present paper, we consider local moves on classical and welded diagrams: (self-)crossing change, (self-)virtualization, virtual conjugation, Delta, fused, band-pass and weld…
On Usual, Virtual and Welded knotted objects up to homotopy
Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan +1
We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either sel…
On the welded Tube map
Benjamin Audoux
This note investigates the so-called Tube map which connects welded knots, that is a quotient of the virtual knot theory, to ribbon torus-knots, that is a restricted notion of fill…
Homotopy classification of ribbon tubes and welded string links
Benjamin Audoux, Paolo Bellingeri, Jean-Baptiste Meilhan +1
Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations…
Khovanov homology and star-like isotopies
Benjamin Audoux
A star-like isotopy for oriented links in 3-space is an isotopy which uses only Reidemeister II moves with opposite orientations and Reidemeister III moves with alternating orienta…
Singular link Floer homology
Benjamin Audoux
We define a grid presentation for singular links i.e. links with a finite number of rigid transverse double points. Then we use it to generalize link Floer homology to singular lin…
A Jones polynomial for braid-like isotopies of oriented links and its categorification
Benjamin Audoux, Thomas Fiedler
A braid-like isotopy for links in 3-space is an isotopy which uses only those Reidemeister moves which occur in isotopies of braids. We define a refined Jones polynomial and its co…