Computing Khovanov-Rozansky homology and defect fusion

DOI10.2140/agt.2014.14.489zbMath1326.57024arXiv1108.1081OpenAlexW3100122017MaRDI QIDQ395755

Nils Carqueville, Daniel Murfet

Publication date: 30 January 2014

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.1081

zbMATH Keywords

topological quantum field theoriesmatrix factorizationsadjunctions in bicategories

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56)

Related Items

Towards \(\mathcal{R}\)-matrix construction of Khovanov-Rozansky polynomials I. Primary \(T\)-deformation of HOMFLY, Introduction to Khovanov homologies. I. Unreduced Jones superpolynomial, Superpolynomials for torus knots from evolution induced by cut-and-join operators, HOMFLY polynomials in representation \([3, 1\) for 3-strand braids], Factorization of differential expansion for antiparallel double-braid knots, Pushing forward matrix factorizations, Sequencing BPS spectra, Matrix factorisations for rational boundary conditions by defect fusion, Colored HOMFLY polynomials of knots presented as double fat diagrams, Interplay between Macdonald and Hall-Littlewood expansions of extended torus superpolynomials, Orbifold equivalence: structure and new examples, \(\mathfrak{sl}_3\)-foam homology calculations, \(N=2\) minimal conformal field theories and matrix bifactorisations of \(x^d\), Orbifold equivalent potentials, Lectures on knot homology, On supersymmetric interface defects, brane parallel transport, order-disorder transition and homological mirror symmetry, Matrix factorizations, Reality and Knörrer periodicity, Checks of integrality properties in topological strings, Rectangular superpolynomials for the figure-eight knot \(4_1\), Matrix model and dimensions at hypercube vertices, Junctions of surface operators and categorification of quantum groups, Cabling procedure for the colored HOMFLY polynomials, Orbifolds and topological defects, Encodings of Turing machines in linear logic, Cofree coalgebras and differential linear logic, On ambiguity in knot polynomials for virtual knots, Differential hierarchy and additional grading of knot polynomials, Discrete torsion defects, Algebra of quantum \(\mathcal{C} \)-polynomials, Fusion of interfaces in Landau-Ginzburg models: a functorial approach, HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations, On the Landau-Ginzburg/conformal field theory correspondence, 𝔤𝔩n-webs, categorification and Khovanov–Rozansky homologies, Exponential growth of colored HOMFLY-PT homology, Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid

Uses Software

• SINGULAR

Cites Work

• Superpolynomials for torus knots from evolution induced by cut-and-join operators
• Link homologies and the refined topological vertex
• Compact generators in categories of matrix factorizations
• Rigidity and defect actions in Landau-Ginzburg models
• Khovanov-Rozansky homology of two-bridge knots and links
• B-type defects in Landau-Ginzburg models
• Adjunctions and defects in Landau-Ginzburg models
• Some differentials on Khovanov-Rozansky homology
• Matrix factorizations and link homology. II.
• \(sl(N)\)-link homology \((N\geq 4)\) using foams and the Kapustin-Li formula
• Homfly polynomial via an invariant of colored plane graphs
• Ribbon graphs and their invariants derived from quantum groups
• Pushing forward matrix factorizations
• Khovanov-Rozansky homology and topological strings
• Khovanov-Rozansky homology via a canopolis formalism
• Topological Landau-Ginzburg models on the world-sheet foam
• Knot homology and refined Chern-Simons index
• Topological Field Theory, Higher Categories, and Their Applications
• Field theories with defects and the centre functor
• The Superpolynomial for Knot Homologies
• Braids, transversal links and the Khovanov-Rozansky Theory
• On the monoidal structure of matrix bi-factorizations
• TRIPLY-GRADED LINK HOMOLOGY AND HOCHSCHILD HOMOLOGY OF SOERGEL BIMODULES
• Matrix factorizations and link homology
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item