A closed formula for the evaluation of foams

Autor: Louis-Hadrien Robert, Emmanuel Wagner

Publikováno v: Quantum Topology
Quantum Topology, 2020, 11 (3), pp.411-487. ⟨10.4171/QT/139⟩
Quantum Topology, European Mathematical Society Publishing House, 2020, 11 (3), pp.411-487. ⟨10.4171/QT/139⟩

International audience; We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov-Rozansky link homolog

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::41c2acf623b5a2723c793a6110ee2ef4
https://uca.hal.science/hal-04155421

Box-Total Dual Integrality, Box-Integrality, and Equimodular Matrices

Autor: Louis-Hadrien Robert, Patrick Chervet, Roland Grappe

Publikováno v: Mathematical Programming
Mathematical Programming, 2021, 188 (1), pp.319-349. ⟨10.1007/s10107-020-01514-0⟩

Box-totally dual integral (box-TDI) polyhedra are polyhedra described by systems which yield strong min-max relations. We characterize them in several ways, involving the notions of principal box-integer polyhedra and equimodular matrices. A polyhedr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b7f2052c261afacab5d7fc77f3e92ba0
http://orbilu.uni.lu/handle/10993/46625

A signature invariant for knotted Klein graphs

Autor: Catherine Gille, Louis-Hadrien Robert

Publikováno v: Algebr. Geom. Topol. 18, no. 6 (2018), 3719-3747
Algebraic and Geometric Topology
Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2018, 18 (6), pp.3719-3747. ⟨10.2140/agt.2018.18.3719⟩
Algebraic and Geometric Topology, 2018, 18 (6), pp.3719-3747. ⟨10.2140/agt.2018.18.3719⟩

We define some signature invariants for a class of knotted trivalent graphs using branched covers. We relate them to classical signatures of knots and links. Finally, we explain how to compute these invariants through the example of Kinoshita's knott

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b0e827522f1d15ff7b9fc34e1421c3f
https://projecteuclid.org/euclid.agt/1540605655

Grothendieck groups of the Khovanov-Kuperberg algebras

Autor: Louis-Hadrien Robert

Publikováno v: Journal of Knot Theory and Its Ramifications
Journal of Knot Theory and Its Ramifications, 2015, 24 (14), pp.1550070. ⟨10.1142/S0218216515500704⟩

The aim of this note is to take benefit of the foam nature of the Khovanov-Kuperberg algebras to compute the Grothendieck groups of their categories of finitely generated projective modules. The computation relies on the Hattori-Stallings trace and s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::266ea9735f6da9b95faf6b1ecd1f6bff

A large family of indecomposable projective modules for the Khovanov-Kuperberg algebra of $sl_3$-webs

Autor: Louis-Hadrien Robert

Publikováno v: Journal of Knot Theory and Its Ramifications
Journal of Knot Theory and Its Ramifications, 2013, 22 (11), pp.1350062. ⟨10.1142/S0218216513500624⟩

We recall a construction of Mackaay, Pan and Tubbenhauer of the algebras $K^{\epsilon}$ which allow to understand the $sl_3$ homology for links in a local way (i.e. for tangles). Then, by studying the combinatorics of the Kuperberg bracket, we give a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0dc14c16b4778563a4459a9bf4730634
http://arxiv.org/abs/1207.6287