Volume 14, issue 1 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 6, 3145–3787
Issue 5, 2527–3144
Issue 4, 1917–2526
Issue 3, 1265–1915
Issue 2, 645–1264
Issue 1, 1–644

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Computing Khovanov–Rozansky homology and defect fusion

Nils Carqueville and Daniel Murfet

Algebraic & Geometric Topology 14 (2014) 489–537
Bibliography
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