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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Categorified $\mathfrak{sl}_N$ invariants of colored rational tangles

Paul Wedrich

Algebraic & Geometric Topology 16 (2016) 427–482
Bibliography
1 A K Aiston, Skein theoretic idempotents of Hecke algebras and quantum group invariants, PhD thesis, University of Liverpool (1996)
2 D Bar-Natan, Khovanov’s homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443 MR2174270
3 S Bigelow, A homological definition of the Jones polynomial, from: "Invariants of knots and 3–manifolds", Geom. Topol. Monogr. 4 (2002) 29 MR2002601
4 S Bigelow, A homological definition of the HOMFLY polynomial, Algebr. Geom. Topol. 7 (2007) 1409 MR2350288
5 S Cautis, Rigidity in higher representation theory, preprint (2014) arXiv:1409.0827
6 S Cautis, Clasp technology to knot homology via the affine Grassmannian, Math. Ann. 363 (2015) 1053 MR3412353
7 S Cautis, J Kamnitzer, A Licata, Categorical geometric skew Howe duality, Invent. Math. 180 (2010) 111 MR2593278
8 S Cautis, J Kamnitzer, A Licata, Derived equivalences for cotangent bundles of Grassmannians via categorical 𝔰𝔩2 actions, J. Reine Angew. Math. 675 (2013) 53 MR3021447
9 S Cautis, J Kamnitzer, S Morrison, Webs and quantum skew Howe duality, Math. Ann. 360 (2014) 351 MR3263166
10 J Chuang, R Rouquier, Derived equivalences for symmetric groups and 𝔰𝔩2–categorification, Ann. of Math. 167 (2008) 245 MR2373155
11 M Ehrig, C Stroppel, Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality, preprint (2013) arXiv:1310.1972
12 P Freyd, D Yetter, J Hoste, W B R Lickorish, K Millett, A Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. 12 (1985) 239 MR776477
13 S Garoufalidis, The colored HOMFLY polynomial is q–holonomic, preprint (2012) arXiv:1211.6388
14 N Geer, B Patureau-Mirand, On the colored HOMFLY–PT, multivariable and Kashaev link invariants, Commun. Contemp. Math. 10 (2008) 993 MR2468374
15 N Geer, B Patureau-Mirand, Multivariable link invariants arising from Lie superalgebras of type I, J. Knot Theory Ramifications 19 (2010) 93 MR2640994
16 N Geer, B Patureau-Mirand, V Turaev, Modified quantum dimensions and re-normalized link invariants, Compos. Math. 145 (2009) 196 MR2480500
17 B Gornik, Note on Khovanov link cohomology, (2004) arXiv:math/0402266
18 E Gorsky, S Gukov, M Stošić, Quadruply-graded colored homology of knots, preprint (2013) arXiv:1304.3481
19 S Gukov, M Stošić, Homological algebra of knots and BPS states, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18 (2012) 309 MR3084243
20 L H Kauffman, S Lambropoulou, On the classification of rational tangles, Adv. in Appl. Math. 33 (2004) 199 MR2074397
21 M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
22 M Khovanov, Triply-graded link homology and Hochschild homology of Soergel bimodules, Internat. J. Math. 18 (2007) 869 MR2339573
23 M Khovanov, A D Lauda, A diagrammatic approach to categorification of quantum groups, I, Represent. Theory 13 (2009) 309 MR2525917
24 M Khovanov, A D Lauda, A categorification of quantum sl(n), Quantum Topol. 1 (2010) 1 MR2628852
25 M Khovanov, A D Lauda, A diagrammatic approach to categorification of quantum groups, II, Trans. Amer. Math. Soc. 363 (2011) 2685 MR2763732
26 M Khovanov, A D Lauda, M Mackaay, M Stošić, Extended graphical calculus for categorified quantum sl(2), 1029, Amer. Math. Soc. (2012) MR2963085
27 M Khovanov, L Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008) 1 MR2391017
28 M Khovanov, L Rozansky, Matrix factorizations and link homology, II, Geom. Topol. 12 (2008) 1387 MR2421131
29 A D Lauda, A categorification of quantum sl(2), Adv. Math. 225 (2010) 3327 MR2729010
30 A D Lauda, Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties, Algebr. Represent. Theory 14 (2011) 253 MR2776785
31 A D Lauda, An introduction to diagrammatic algebra and categorified quantum 𝔰𝔩2, Bull. Inst. Math. Acad. Sin. 7 (2012) 165 MR3024893
32 A D Lauda, H Queffelec, D E V Rose, Khovanov homology is a skew Howe 2–representation of categorified quantum 𝔰𝔩m, Algebr. Geom. Topol. 15 (2015) 2517 MR3426687
33 R J Lawrence, Homological representations of the Hecke algebra, Comm. Math. Phys. 135 (1990) 141 MR1086755
34 E S Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005) 554 MR2173845
35 S G Lukac, Homfly skeins and the Hopf link, PhD thesis, University of Liverpool (2001)
36 M Mackaay, M Stošić, P Vaz, The 1,2–coloured HOMFLY–PT link homology, Trans. Amer. Math. Soc. 363 (2011) 2091 MR2746676
37 C Manolescu, Nilpotent slices, Hilbert schemes, and the Jones polynomial, Duke Math. J. 132 (2006) 311 MR2219260
38 C Manolescu, Link homology theories from symplectic geometry, Adv. Math. 211 (2007) 363 MR2313538
39 V Mazorchuk, C Stroppel, A combinatorial approach to functorial quantum 𝔰𝔩k knot invariants, Amer. J. Math. 131 (2009) 1679 MR2567504
40 H R Morton, The multivariable Alexander polynomial for a closed braid, from: "Low-dimensional topology" (editor H Nencka), Contemp. Math. 233, Amer. Math. Soc. (1999) 167 MR1701681
41 H R Morton, S G Lukac, The Homfly polynomial of the decorated Hopf link, J. Knot Theory Ramifications 12 (2003) 395 MR1983094
42 H Murakami, T Ohtsuki, S Yamada, Homfly polynomial via an invariant of colored plane graphs, Enseign. Math. 44 (1998) 325 MR1659228
43 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
44 D E V Rose, P Wedrich, Deformations of colored 𝔰𝔩(N) link homologies via foams, preprint (2015) arXiv:1501.02567
45 L Rozansky, An infinite torus braid yields a categorified Jones–Wenzl projector, Fund. Math. 225 (2014) 305 MR3205575
46 P Seidel, I Smith, A link invariant from the symplectic geometry of nilpotent slices, Duke Math. J. 134 (2006) 453 MR2254624
47 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 167 (1988) 79, 190 MR964255
48 P Turner, A hitchhiker’s guide to Khovanov homology, preprint (2014) arXiv:1409.6442
49 B Webster, G Williamson, A geometric construction of colored HOMFLYPT homology, preprint (2010) arXiv:0905.0486
50 P Wedrich, q–holonomic formulas for colored HOMFLY polynomials of 2–bridge links, preprint (2014) arXiv:1410.3769
51 E Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351 MR990772
52 H Wu, A colored 𝔰𝔩(N) homology for links in S3, Dissertationes Math. (Rozprawy Mat.) 499 (2014) MR3234803