Benjamin Audoux
{webpage}
My research field concerns knot theory
in particular and low dimensional topology in general. I
began in classical knot theory. During my PhD, I worked on
Khovanov and Heegaard-Floer homologies; I generalized their
constructions, the former to some diagrammatic notion of
constrained links, and the latter to topological
singular links. Now, my research essentially focusses on the
study of combinatorial models emerging from topology,
and their application to topology and to other fields of mathematics.
Thus far, my main research field
concerns the combinatorial aspects of knotted surfaces in
dimension 4, et especially their study via cut-diagrams. But
I still keep some interests in 3-dimensional topology,
including finite type invariants. Beside that, I work on
applications of topological tools in other fields. My main
contributions are on quantum code theory,
constructing quantum error correcting code families.
{submitted}
A universal finite type invariant of knots in
homology 3-spheres
in collaboration with D. Moussard
arXiv:2209.00473, hal-03778247
Milnor concordance invariant for knotted surfaces and beyond
in collaboration with J-B. Meilhan and Y. Yasuhara
arXiv:2109.14578,
hal-03359997
{published}
Welded graphs, Wirtinger
groups and knotted punctured spheres
in collaboration with J-B. Meilhan and Y. Yasuhara
arXiv:2311.01922, hal-04272362
to be published as a chapter in
Essays on topology: Dedicated to Valentin Poénaru, eds
L. Funar and A. Papadopoulos
Higher order Kirk invariants of link maps
in collaboration with J-B. Meilhan and Y. Yasuhara
arXiv:2311.03015, hal-04273743
to be published in
Indiana University Mathematical Journal
k-reduced groups and Milnor invariants
in collaboration with J-B. Meilhan and Y. Yasuhara
arXiv:2205.04768, hal-03691863
à paraître dans
Mathematical Research Letters
Characterization of the reduced peripheral system of links
in collaboration with J-B. Meilhan
arXiv:1904.04763, hal-02094675
Journal of the Institute of
Mathématics of Jussieu 23, issue 6, p.2441–2459
Toward universality in degree 2 of the Kricker lift
of the Kontsevich integral and the Lescop equivariant invariant
in collaboration with D. Moussard
arXiv:1710.09730, hal-01624563
International Journal of Mathematics 30, issue 5, 1950021 (37 pages)
On tensor products of CSS codes
in collaboration with A. Couvreur
arXiv:1512.07081, hal-01248760
Annales de l'Institut Henri Poincaré D 6, issue 2, p. 239-287
Extensions of some classical local moves on knot diagrams
extended version of the former paper "On forbidden moves and the
Delta move"
in collaboration with P. Bellingeri, J-B. Meilhan and E. Wagner
arXiv:1510.04237, hal-01217085
Michigan Mathematical Journal 67, issue 3, p. 647-672
On multiplicity of eigenvalues and symmetry
of eigenfunctions of the p-Laplacian
in collaboration with V. Bobkov and E. Parini
arXiv:1704.03194, hal-01505548
Topological Methods in Nonlinear Analysis
51, issue 2, p. 565-582
On hyperbolic knots in S3 with exceptional surgeries at maximal distance
in collaboration with A. G. Lecuona and F. Roukema
arXiv:1701.01751, hal-01485358
Algebraic and Geometric Topology 18, issue 4, p. 2371-2417
On codimension two embeddings up to link-homotopy
in collaboration with J-B. Meilhan and E. Wagner
arXiv:1703.07999, hal-01504996
Journal of Topology 10, issue 4, p. 1107-1123
On usual, virtual and welded knotted objects up to homotopy
in collaboration with P. Bellingeri, J-B. Meilhan and E. Wagner
arXiv:1507.00202, hal-01176073
Journal of the Mathematical Society of
Japan 69, issue 3, p. 1079-1097
Homotopy classification of ribbon tubes and welded string links
in collaboration with P. Bellingeri, J-B. Meilhan and E. Wagner
arXiv:1407.0184, hal-01017350
Annali della Scuola Normale Superiore di
Pisa Classe di Scienza 17, issue 2, p. 713-761
On the welded Tube map
arXiv:1408.5479, hal-01066617
Contemporary Mathematics 670, p. 261-284
Rasmussen invariant and Milnor conjecture
lecture notes
hal-01208217
Winter
Braids Lecture Notes: Winter Braids IV (Dijon, 2014) (2014), Exp. No. 1, 19p.
An application of Khovanov homology to quantum codes
arXiv:1307.4677, hal-01066619
Annales de l'Institut Henri Poincaré D 1, issue 2, p. 185-223
Surfaces with pulleys and Khovanov homology
hal-01217084
Journal of
Knot Theory and its Ramifications 20, issue 7, p. 1021-1040
Singular link Floer homology
arXiv:0705.2377, hal-01217083
Algebraic & Geometric Topology 9, p. 495-535
Khovanov homology and star-like isotopies
arXiv:0804.1292, hal-00626873
Topology and its Applications 156, issue 6, p. 1054-1070
A Jones polynomial for braid-like isotopies of oriented links and its categorification
in collaboration with T. Fiedler
arXiv:math/0503080, hal-00012105
Algebraic & Geometric Topology 5, p. 1535-1553
Généralisation de l'homologie d'Heegaard-Floer aux entrelacs singuliers
& Raffinement de l'homologie de Khovanov aux entrelacs restreints
Ph.D. thesis, defended on december 5th, 2007 at Université Paul Sabatier, Toulouse
arXiv:0803.4478
Applications de modèles combinatoires issus de la topologie
habilitation, defended on february 16th, 2018 at Aix-Marseille Université