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We study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane).
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J.M.F. Labastida, M. Mariño and C. Vafa, Knots, links and branes at large N
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H. Ooguri, C. Vafa, Knot invariants and topological strings
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T. Ekedahl, S. Lando, M. Shapiro and A. Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves
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2001
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C.H. Taubes, Lagrangians for the Gopakumar-Vafa conjecture
2001
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A. Aganagic, A. Klemm, C. Vafa, Disk instantons, mirror symmetry and the duality web
2002
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J.M.F. Labastida and M. Mariño, A new point of view in the theory of knot and link invariants
2002
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M. Mariño, C. Vafa, Framed knots at large N
2002
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V. Bouchard, A. Klemm, M. Mariño, and S. Pasquetti, Remodeling the B-model
2009
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J. Li, C.-C. Liu, K. Liu, J. Zhou, A mathematical theory of the topological vertex
2009
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K. Liu and P. Peng, Proof of the Labastida-Mariño-Ooguri-Vafa conjecture
2010
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X.-S. Lin and H. Zheng, On the Hecke algebra and the colored HOMFLY polynomial
2010
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J. Zhou, A proof of the full Mariõ-Vafa conjecture
2010
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M. Kontsevich, Y. Soibelman, Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
2011
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C.-C. Liu, K. Liu, J. Zhou, A proof of a conjecture of Mariño-Vafa on Hodge integrals
2003
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M. Aganagic, M. Marino, C. Vafa, All loop topological string amplitudes from Chern-Simons theory
2004
Cited alongside, same era.
A. Okounkov, R. Pandharipande, Hodge integrals and invariants of the unknot
2004
Cited alongside, same era.
M. Aganagic, A. Klemm, M. Mariño and C. Vafa, The topological vertex
2005
Cited alongside, same era.
S. Garoufalidis and T.T.Q. Le, The colored Jones function is q-holonomic
2005
Cited alongside, same era.
Y. Konishi, Integrality of Gopakumar-Vafa invariants of toric Calabi-Yau threefolds
2006
Cited alongside, same era.
K. Liu and P. Peng, New structures of knot invariants
2011
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D. Maulik, A. Oblomkov, A. Okounkov and R. Pandharipande Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
2011
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H. Fuji, S. Gukov, P. Sulkowski, H. Awata, Volume Conjecture: Refined and Categorified
2012
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M. Reineke, Degenerate Cohomological Hall algebra and quantized Donaldson-Thomas invariants for m-loop quivers
2012
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S. Zhu, Hodge Integral Identities from the Cut-and-Join Equation of Mariño-Vafa formula
2012
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D.-E. Diaconescu, V. Shende and C. Vafa, Large N duality, lagrangian cycles, and algebraic knots
2013
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H. Fuji, S. Gukov, P. Sulkowski, Super-A-polynomial for knots and BPS states
2013
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B. Fang, C.-C., M Liu, Open Gromov-Witten invariants of toric Calabi-Yau 3-folds
2013
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S. Zhu, Colored HOMFLY polynomials via skein theory
2013
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A. Mironov, A. Morozov, An. Morozov, On colored HOMFLY polynomials for twist knots
2014
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E. Eynard and N. Orantin, Computation of open Gromov-Witten invariants for toric Calabi- Yau 3-folds by topological recursion, a proof of the BKMP conjecture
2015
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S. Garoufalidis, P. Kucharski and P. Sulkowski, Knots, BPS states, and algebraic curves
2016
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