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The paper introduces Slope Conjecture which relates the degree of the Jones polynomial of a knot and its parallels with the slopes of incompressible surfaces in the knot complement.
E. Ehrhart, Sur les polyèdres homothétiques bordés à n n dimensions
1962
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A.E. Hatcher, On the boundary curves of incompressible surfaces
1982
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by same authorand P.B. Shalen, Bounded, separating, incompressible surfaces in knot manifolds
1984
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D. Mermin, Is the moon there when nobody looks? Reality and the quantum theory
1985
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by same author, C.McA. Gordon, J. Luecke and P.B. Shalen, Dehn surgery on knots
1987
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V.F.R. Jones, Hecke algebra representations of braid groups and link polynomials
1987
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L.H. Kauffman, State models and the Jones polynomial
1987
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K. Murasugi, Jones polynomials and classical conjectures in knot theory
1987
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M.B. Thistlethwaite, A spanning tree expansion of the Jones polynomial
1987
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V. Turaev, A simple proof of the Murasugi and Kauffman theorems on alternating links
1987
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by same authorand M.B. Thistlethwaite, Some links with nontrivial polynomials and their crossing-numbers
1988
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by same author, The Yang-Baxter equation and invariants of links
1988
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by same authorand U. Oertel, Boundary slopes for Montesinos knots
1989
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D. Zeilberger, A holonomic systems approach to special functions identities
1990
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H. Wilf and D. Zeilberger, An algorithmic proof theory for hypergeometric (ordinary and q q ) multisum/integral identities
1992
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D. Cooper, D, M. Culler, H. Gillet, D. Long and P. Shalen, Plane curves associated to character varieties of 3 3 -manifolds
1994
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by same authorand S.L. Lins, Temperley-Lieb recoupling theory and invariants of 3 3 -manifolds
1994
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S. Carter, D.E. Flath, M. Saito, The Classical and Quantum 6 j 6j -symbols
1995
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J.C. Jantzen, Lecture on quantum groups
1995
Earlier work this paper cites.
H.R. Morton, The coloured Jones function and Alexander polynomial for torus knots
1995
Cited alongside, same era.
by same authorand S. Garoufalidis, On the Melvin-Morton-Rozansky conjecture
1996
Cited alongside, same era.
M. Brion and M. Vergne, Lattice points in simple polytopes
1997
Cited alongside, same era.
R. Kashaev, The hyperbolic volume of knots from the quantum dilogarithm
1997
Cited alongside, same era.
W.B.R. Lickorish, An introduction to knot theory
1997
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R.P. Stanley, Enumerative Combinatorics, Volume 1
1997
Cited alongside, same era.
J. Zhu, On Kauffman brackets
T.T.Q. Le, The colored Jones polynomial and the A A -polynomial of knots
2006
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M. Beck and S. Robins, Computing the continuous discretely, Integer-point enumeration in polyhedra
2007
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S. Matveev, Algorithmic topology and classification of 3-manifolds
2007
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D. Futer, E. Kalfagianni and J.S. Purcell, Dehn filling, volume, and the Jones polynomial
2008
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M. Hedden and P. Ording, The Ozsváth-Szabó and Rasmussen concordance invariants are not equal
2008
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K. Ichihara and S. Mizushima, Crossing number and diameter of boundary slope set of Montesinos knot
2008
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1997
Cited alongside, same era.
A. Barvinok and J.E. Pommersheim, An algorithmic theory of lattice points in polyhedra
1999
Cited alongside, same era.
N.M. Dunfield, A table of boundary slopes of Montesinos knots
2001
Cited alongside, same era.
by same author, The Culler-Shalen seminorms of the ( − 2 , 3 , n ) (-2,3,n) pretzel knot
2002
Cited alongside, same era.
P. Ozsváth and Z. Szabó, On the Floer homology of plumbed three-manifolds
2003
Cited alongside, same era.
by same authorand R. Lawrence, A rational surgery formula for the LMO invariant
2004
Cited alongside, same era.
Later among the works it cites.
2008
Later among the works it cites.
F. Luo and S. Tillmann, Angle structures and normal surfaces
2008
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T.W. Mattman, G. Maybrun and K. Robinson, 2-bridge knot boundary slopes: diameter and genus
2008
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F. Costantino, Integrality of Kauffman brackets of trivalent graphs
2009
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C.L. Curtis and S. Taylor, The Jones polynomial and boundary slopes of alternating knots
2009
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by same authorand R. van der Veen, Asymptotics of quantum spin networks at a fixed root of unity
2009
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2009
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by same authorand S. Garoufalidis, Boundary slopes of 1-cusped manifolds
2010
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by same author, The degree of a q q -holonomic sequence is a quadratic quasi-polynomial
2010
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by same author, Tropicalization and the Slope Conjecture for 2-fusion knots
2010
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by same author, Knots and tropical curves
2010
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by same authorand T. Vuong, The Slope Conjecture for Simple Lie algebras
2010
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