On a proof of the Labastida-Marino-Ooguri-Vafa conjecture
Abstract
We outline a proof of a remarkable conjecture of Labastida-Mari\~no-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.
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