Matrix Factorizations and Kauffman Homology

2005/12/22 by Sergei Gukov, Gukov, Sergei, Johannes Walcher +1 · 3 citations
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/0512298

openalex publication_date 2005/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants

Cited by

• Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Link homology theories from symplectic geometry

Related

• Notes on matrix factorizations and knot homology
• Kauffman states, bordered algebras, and a bigraded knot invariant
• Step by step categorification of the Jones polynomial in Kauffman's version
• Colored sl(N) link homology via matrix factorizations
• Matrix factorizations and link homology