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Computing Khovanov–Rozansky homology and defect fusion

Nils Carqueville and Daniel Murfet

Algebraic & Geometric Topology 14 (2014) 489–537
1 M Aganagic, S Shakirov, Knot homology from refined Chern–Simons theory, arXiv:1105.5117
2 H Becker, Khovanov–Rozansky homology via Cohen–Macaulay approximations and Soergel bimodules, arXiv:1105.0702
3 I Brunner, D Roggenkamp, B–type defects in Landau–Ginzburg models, J. High Energy Phys. (2007) 093 MR2342020
4 N Carqueville, D Murfet, Code to compute Khovanov–Rozansky homology and defect fusion in Landau–Ginzburg models,
5 N Carqueville, I Runkel, On the monoidal structure of matrix bi-factorizations, J. Phys. A 43 (2010) 275401, 33 MR2658288
6 N Carqueville, I Runkel, Rigidity and defect actions in Landau–Ginzburg models, Comm. Math. Phys. 310 (2012) 135 MR2885616
7 M Crainic, On the perturbation lemma, and deformations, arXiv:math.AT/0403266
8 A Davydov, L Kong, I Runkel, Field theories with defects and the centre functor, from: "Mathematical foundations of quantum field theory and perturbative string theory" (editors H Sati, U Schreiber), Proc. Sympos. Pure Math. 83, Amer. Math. Soc. (2011) 71 MR2742426
9 N M Dunfield, S Gukov, J Rasmussen, The superpolynomial for knot homologies, Experiment. Math. 15 (2006) 129 MR2253002
10 P Dunin-Barkowski, A Mironov, A Morozov, Sleptsov,A., A Smirnov, Superpolynomials for toric knots from evolution induced by cut-and-join operators, arXiv:1106.4305
11 T Dyckerhoff, Compact generators in categories of matrix factorizations, Duke Math. J. 159 (2011) 223 MR2824483
12 T Dyckerhoff, D Murfet, Pushing forward matrix factorisations, arXiv:1102.2957
13 S Gukov, A Iqbal, C Kozçaz, C Vafa, Link homologies and the refined topological vertex, Comm. Math. Phys. 298 (2010) 757 MR2670927
14 S Gukov, A Schwarz, C Vafa, Khovanov–Rozansky homology and topological strings, Lett. Math. Phys. 74 (2005) 53 MR2193547
15 T C Jaeger, Khovanov–Rozansky homology and Conway mutation, arXiv:1101.3302
16 A Kapustin, Topological field theory, higher categories, and their applications, arXiv:1004.2307
17 A Kawauchi, A survey of knot theory, Birkhäuser (1996) MR1417494
18 M Khovanov, Triply-graded link homology and Hochschild homology of Soergel bimodules, Internat. J. Math. 18 (2007) 869 MR2339573
19 M Khovanov, L Rozansky, Topological Landau–Ginzburg models on the world-sheet foam, Adv. Theor. Math. Phys. 11 (2007) 233 MR2322554
20 M Khovanov, L Rozansky, Virtual crossings, convolutions and a categorification of the $\mathrm{SO}(2N)$ Kauffman polynomial, J. Gökova Geom. Topol. GGT 1 (2007) 116 MR2386537
21 M Khovanov, L Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008) 1 MR2391017
22 M Khovanov, L Rozansky, Matrix factorizations and link homology, II, Geom. Topol. 12 (2008) 1387 MR2421131
23 J Lambek, Lectures on rings and modules, Chelsea Publishing (1976) MR0419493
24 C I Lazaroiu, D McNamee, unpublished
25 M Mackaay, M Stošić, P Vaz, $\mathfrak{sl}(N)$–link homology $(N\geq 4)$ using foams and the Kapustin–Li formula, Geom. Topol. 13 (2009) 1075 MR2491657
26 D McNamee, On the mathematical structure of topological defects in Landau–Ginzburg models, master’s thesis, Trinity College Dublin (2009)
27 H Murakami, T Ohtsuki, S Yamada, Homfly polynomial via an invariant of colored plane graphs, Enseign. Math. 44 (1998) 325 MR1659228
28 J Rasmussen, Some differentials on Khovanov–Rozansky homology, arXiv:math.GT/0607544
29 J Rasmussen, Khovanov–Rozansky homology of two-bridge knots and links, Duke Math. J. 136 (2007) 551 MR2309174
30 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
31 J Rickard, Translation functors and equivalences of derived categories for blocks of algebraic groups, from: "Finite-dimensional algebras and related topics" (editors V Dlab, L L Scott), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424, Kluwer Acad. Publ. (1994) 255 MR1308990
32 R Rouquier, Categorification of $\mathfrak{sl}_2$ and braid groups, from: "Trends in representation theory of algebras and related topics" (editors J A de la Peña, R Bautista), Contemp. Math. 406, Amer. Math. Soc. (2006) 137 MR2258045
33 B Webster, Khovanov–Rozansky homology via a canopolis formalism, Algebr. Geom. Topol. 7 (2007) 673 MR2308960
34 H Wu, A colored $\mathfrak{sl}(N)$–homology for links in $S^3$, arXiv:0907.0695
35 H Wu, Braids, transversal links and the Khovanov–Rozansky theory, Trans. Amer. Math. Soc. 360 (2008) 3365 MR2386230