On a proof of the Labastida-Marino-Ooguri-Vafa conjecture

Abstract

We outline a proof of a remarkable conjecture of Labastida-Mari{ñ}o-Ooguri-Vafa about certain new algebraic structures of quantum link invariants and the integrality of infinite family of new topological invariants. Our method is based on the cut-and-join analysis and a special rational ring characterizing the structure of the Chern-Simons partition function.

References in corpus (4)

• Topological String Partition Functions as Polynomials
• Topological Open String Amplitudes On Orientifolds
• On the volume conjecture for small angles
• Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cut

Cited by in corpus (9)

• Link Homologies and the Refined Topological Vertex
• Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
• On genus expansion of knot polynomials and hidden structure of Hurwitz tau-functions
• Differential expansion and rectangular HOMFLY for the figure eight knot
• On Factorization of Generalized Macdonald Polynomials
• q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links
• Proof of the Labastida-Marino-Ooguri-Vafa Conjecture
• A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras
• Geometry As Seen By String Theory