Mathematical Research Letters

Volume 17 (2010)

Number 6

A Proof of the Full Mariño-Vafa Conjecture

Pages: 1091 – 1099

DOI: http://dx.doi.org/10.4310/MRL.2010.v17.n6.a8

Author

Jian Zhou (Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China)

Abstract

We present a proof of the full Mariño-Vafa Conjecture that identifies certain open string invariants of the resolved conifold with the Chern-Simons knot invariant of the unknot, i.e. the quantum dimensions. This proof is based on earlier works \cite{LLZ1, Oko-Pan, LLZ2} that culminate in a mathematical theory of the topological vertex \cite{LLLZ}.

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