Matrix Factorizations and Kauffman Homology

Abstract

The topological string interpretation of homological knot invariants has led to several insights into the structure of the theory in the case of sl(N). We study possible extensions of the matrix factorization approach to knot homology for other Lie groups and representations. In particular, we introduce a new triply graded theory categorifying the Kauffman polynomial, test it, and predict the Kauffman homology for several simple knots.

45 pages, harvmac

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Cited by in corpus (28)

• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Super-A-polynomial for knots and BPS states
• Link Homologies and the Refined Topological Vertex
• Surface Operators and Knot Homologies
• Deformations of colored sl(N) link homologies via foams
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Changing the preferred direction of the refined topological vertex
• String theory and the Kauffman polynomial
• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• Colored Kauffman Homology and Super-A-polynomials
• D-branes as a Bubbling Calabi-Yau
• Orientifolds and the Refined Topological String
• Macdonald operators and homological invariants of the colored Hopf link
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Matrix Factorizations, D-Branes and their Deformations
• Link homology and categorification
• Holography, Matrix Factorizations and K-stability
• Challenges of beta-deformation
• D-Branes in Topological String Theory
• Composite Representation Invariants and Unoriented Topological String Amplitudes
• Composite Invariants and Unoriented Topological String Amplitudes
• On stable Khovanov homology of torus knots
• Knot Complement, ADO-Invariants and their Deformations for Torus Knots
• Cyclotomic expansion and volume conjecture for superpolynomials of colored HOMFLY-PT homology and colored Kauffman homology
• On knots, complements, and 6j-symbols
• A categorification of the quantum sl(N)-link polynomials using foams
• Matrix factorizations and double line in ${\mathfrak{sl}}_n$ quantum link invariant
• Link homology theories from symplectic geometry