Mathematical Research Letters

Volume 17 (2010)

Number 3

On a proof of the Labastida-Mariño-Ooguri-Vafa Conjecture

Pages: 493 – 506



Kefeng Liu (University of California at Los Angeles)

Pan Peng (University of Arizona)


We outline a proof of a remarkable conjecture of Labastida-Mariño-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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