1 |
M Aganagic, S
Shakirov, Knot homology from refined Chern–Simons
theory arXiv:1105.5117 |
2 |
O Aharony, S S
Gubser, J Maldacena, H Ooguri, Y Oz,
Large N field
theories, string theory and gravity, Phys. Rep. 323
(2000) 183–386 MR1743597 |
3 |
D Bar-Natan,
Khovanov's homology for tangles and cobordisms (2005)
arXiv:math/0410495v2 |
4 |
K Behrend, J
Bryan, B Szendrői, Motivic degree
zero Donaldson–Thomas invariants, Invent. Math.
192 (2013) 111–160 MR3032328 |
5 |
I Brunner, M
Herbst, W Lerche, B Scheuner, Landau–Ginzburg
realization of open string TFT, J. High Energy Phys.
(2006) 043 MR2270412 |
6 |
I Brunner, D
Roggenkamp, B–type
defects in Landau–Ginzburg models, J. High Energy
Phys. (2007) 093 MR2342020 |
7 |
S Cecotti, C
Vafa, BPS wall crossing and topological strings
arXiv:0910.2615 |
8 |
B Cooper, M
Hogancamp, V Krushkal, SO(3) homology of
graphs and links, Algebr. Geom. Topol. 11 (2011)
2137–2166 MR2826934 |
9 |
B Cooper, V
Krushkal, Categorification of the
Jones–Wenzl projectors, Quantum Topol. 3 (2012)
139–180 MR2901969 |
10 |
F Denef, G
Moore, Split states, entropy enigmas, holes and
halos (2007) arXiv:hep-th/0702146v2 |
11 |
T Dimofte, S
Gukov, Refined, motivic,
and quantum, Lett. Math. Phys. 91 (2010) 1–27
MR2577296 |
12 |
T Dimofte, S
Gukov, L Hollands, Vortex counting
and Lagrangian 3–manifolds, Lett. Math. Phys. 98
(2011) 225–287 MR2852983 |
13 |
T Dimofte, S
Gukov, Y Soibelman, Quantum wall
crossing in N=2 gauge theories, Lett. Math. Phys. 95
(2011) 1–25 MR2764330 |
14 |
N M Dunfield,
S Gukov, J Rasmussen, The
superpolynomial for knot homologies, Experiment. Math.
15 (2006) 129–159 MR2253002 |
15 |
P Dunin-Barkowski,
A Mironov, A Morozov, A Sleptsov, A
Smirnov, Superpolynomials for toric knots from evolution
induced by cut-and-join operators arXiv:1106.4305 |
16 |
I Frenkel, C
Stroppel, J Sussan, Categorifying fractional
Euler characteristics, Jones–Wenzl projectors and
3j–symbols, Quantum Topol. 3 (2012) 181–253
MR2901970 |
17 |
D Gaiotto, E
Witten, Knot invariants from four-dimensional gauge
theory arXiv:1106.4789 |
18 |
R Gopakumar, C
Vafa, On the gauge theory/geometry correspondence,
Adv. Theor. Math. Phys. 3 (1999) 1415–1443 MR1796682 |
19 |
B Gornik, Note on
Khovanov link cohomology arXiv:math/0402266 |
20 |
E Gorsky, S
Gukov, M Stošić, work in
progress |
21 |
S Gukov, Gauge theory and
knot homologies, Fortschr. Phys. 55 (2007)
473–490 MR2331918 |
22 |
S Gukov, A
Iqbal, C Kozçaz, C Vafa, Link homologies
and the refined topological vertex, Comm. Math. Phys.
298 (2010) 757–785 MR2670927 |
23 |
S Gukov, A
Schwarz, C Vafa, Khovanov–Rozansky
homology and topological strings, Lett. Math. Phys. 74
(2005) 53–74 MR2193547 |
24 |
S Gukov, J
Walcher, Matrix factorizations and Kauffman homology
arXiv:hep-th/0512298 |
25 |
S Gukov, E
Witten, Rigid surface
operators, Adv. Theor. Math. Phys. 14 (2010)
87–177 MR2684979 |
26 |
J A Harvey, G
Moore, On the algebras of
BPS states, Comm. Math. Phys. 197 (1998) 489–519
MR1652775 |
27 |
K Hori, J
Walcher, F–term
equations near Gepner points, J. High Energy Phys.
(2005) 008 MR2134919 |
28 |
A Iqbal, C
Kozçaz, Refined Hopf link revisited, J. High
Energy Phys. (2012) 046 MR2967625 |
29 |
D Jafferis, G
Moore, Wall crossing in local Calabi Yau manifolds
arXiv:0810.4909 |
30 |
A Kapustin, Y
Li, D–branes
in Landau–Ginzburg models and algebraic geometry,
J. High Energy Phys. (2003) 005 MR2041170 |
31 |
A Kapustin, E
Witten, Electric-magnetic duality and the geometric
Langlands program, Commun. Number Theory Phys. 1 (2007)
1–236 MR2306566 |
32 |
M Khovanov, Link
homology and Frobenius extensions arXiv:math/0411447 |
33 |
M Khovanov,
A
categorification of the Jones polynomial, Duke Math. J.
101 (2000) 359–426 MR1740682 |
34 |
M Khovanov,
Triply-graded
link homology and Hochschild homology of Soergel
bimodules, Internat. J. Math. 18 (2007) 869–885
MR2339573 |
35 |
M Khovanov, L
Rozansky, Topological
Landau–Ginzburg models on the world-sheet foam,
Adv. Theor. Math. Phys. 11 (2007) 233–259 MR2322554 |
36 |
M Khovanov, L
Rozansky, Virtual crossings, convolutions and a
categorification of the SO(2N) Kauffman polynomial, J.
Gökova Geom. Topol. GGT 1 (2007) 116–214 MR2386537 |
37 |
M Khovanov, L
Rozansky, Matrix factorizations and
link homology, Fund. Math. 199 (2008) 1–91
MR2391017 |
38 |
M Khovanov, L
Rozansky, Matrix
factorizations and link homology. II, Geom. Topol. 12
(2008) 1387–1425 MR2421131 |
39 |
, The Knot Atlas |
40 |
M Kontsevich, Y
Soibelman, Stability structures, motivic
Donaldson–Thomas invariants and cluster
transformations arXiv:0811.2435 |
41 |
M Kontsevich, Y
Soibelman, Cohomological Hall algebra, exponential Hodge
structures and motivic Donaldson–Thomas invariants,
Commun. Number Theory Phys. 5 (2011) 231–352 MR2851153 |
42 |
S Koshkin, Conormal
bundles to knots and the Gopakumar–Vafa
conjecture, Adv. Theor. Math. Phys. 11 (2007)
591–634 MR2354076 |
43 |
J M F
Labastida, M Mariño, C Vafa, Knots, links
and branes at large N, J. High Energy Phys. (2000) 42
MR1806596 |
44 |
E S Lee,
Khovanov's invariants for alternating links arXiv:math/0210213 |
45 |
X S Lin, H
Zheng, On the Hecke
algebras and the colored HOMFLY polynomial, Trans.
Amer. Math. Soc. 362 (2010) 1–18 MR2550143 |
46 |
K Liu, P Peng,
New structure of knot invariants arXiv:1012.2636 |
47 |
M M, V C,
Framed knots at large N arXiv:hep-th/0108064 |
48 |
M Mackaay, M
Stošić, P Vaz, The
1,2–coloured HOMFLY-PT link homology, Trans.
Amer. Math. Soc. 363 (2011) 2091–2124 MR2746676 |
49 |
E J Mlawer,
S G Naculich, H A Riggs, H J
Schnitzer, Group-level
duality of WZW fusion coefficients and Chern–Simons link
observables, Nuclear Phys. B 352 (1991) 863–896
MR1098252 |
50 |
S G Naculich,
H A Riggs, H J Schnitzer, Group-level
duality in WZW models and Chern–Simons theory,
Phys. Lett. B 246 (1990) 417–422 MR1071916 |
51 |
S G Naculich,
H J Schnitzer, Duality
between SU(N)k and SU(k)N WZW
models, Nuclear Phys. B 347 (1990) 687–742
MR1079689 |
52 |
K Nagao, H
Nakajima, Counting invariant of
perverse coherent sheaves and its wall-crossing, Int.
Math. Res. Not. 2011 (2011) 3885–3938 MR2836398 |
53 |
A Okounkov, N
Reshetikhin, C Vafa, Quantum Calabi–Yau and
classical crystals arXiv:hep-th/0309208 |
54 |
H Ooguri, C
Vafa, Knot
invariants and topological strings, Nuclear Phys. B 577
(2000) 419–438 MR1765411 |
55 |
D Orlov,
Triangulated categories of singularities and D–branes
in Landau–Ginzburg orbifold arXiv:math/0302304 |
56 |
N Reshetikhin,
V G Turaev, Invariants of
3–manifolds via link polynomials and quantum
groups, Invent. Math. 103 (1991) 547–597 MR1091619 |
57 |
O Schiffmann,
Lectures on Hall algebras arXiv:math/0611617 |
58 |
C H Taubes,
Lagrangians for the
Gopakumar–Vafa conjecture, from: "The interaction
of finite-type and Gromov–Witten invariants" (editors D
Auckly, J Bryan), Geom. Topol. Monogr. 8 (2006) 73–95
MR2402820 |
59 |
P Turner,
Calculating Bar-Natan's characteristic-two Khovanov
homology arXiv:math/0411225 |
60 |
B Webster, Knot
invariants and higher representation theory II: the
categorification of quantum knot invariants arXiv:1005.4559 |
61 |
E Witten, Quantum field
theory and the Jones polynomial, Comm. Math. Phys. 121
(1989) 351–399 MR990772 |
62 |
E Witten, Monopoles
and four-manifolds, Math. Res. Lett. 1 (1994) 769–796
MR1306021 |
63 |
E Witten, The
Verlinde algebra and the cohomology of the Grassmannian,
from: "Geometry, topology, & physics" (editor S T
Yau), Conf. Proc. Lecture Notes Geom. Topology 4, Int. Press,
Cambridge, MA (1995) 357–422 MR1358625 |
64 |
E Witten, Fivebranes and knots,
Quantum Topol. 3 (2012) 1–137 MR2852941 |
65 |
H Wu, A colored
sl(N)–homology for links in S³ arXiv:0907.0695 |
66 |
Y Yonezawa, Quantum
(sl(N), ∧ Vn) link invariant and matrix
factorizations arXiv:0906.0220 |