Algebraic & Geometric Topology Volume 13, issue 6 (2013)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

$\mathfrak{sl}_3$–foam homology calculations

Lukas Lewark

Algebraic & Geometric Topology 13 (2013) 3661–3686

DOI: 10.2140/agt.2013.13.3661

Bibliography

1	S Akbulut, Cappell–Shaneson homotopy spheres are standard, Ann. of Math. 171 (2010) 2171 MR2680408
2	D Bar-Natan, Khovanov's homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443 MR2174270
3	D Bar-Natan, Fast Khovanov homology computations, J. Knot Theory Ramifications 16 (2007) 243 MR2320156
4	C Blanchet, N Habegger, G Masbaum, P Vogel, Topological quantum field theories derived from the Kauffman bracket, Topology 34 (1995) 883 MR1362791
5	N Carqueville, D Murfet, Computing Khovanov–Rozansky homology and defect fusion arXiv:1108.1081
6	A Champanerkar, I Kofman, Twisting quasi-alternating links, Proc. Amer. Math. Soc. 137 (2009) 2451 MR2495282
7	M Freedman, Complexity classes as mathematical axioms, Ann. of Math. 170 (2009) 995 MR2552117
8	M Freedman, R Gompf, S Morrison, K Walker, Man and machine thinking about the smooth $4$–dimensional Poincaré conjecture, Quantum Topol. 1 (2010) 171 MR2657647
9	C M Gordon, R A Litherland, On the signature of a link, Invent. Math. 47 (1978) 53 MR0500905
10	J Green, S Morrison, JavaKh (2005)
11	J Greene, Homologically thin, non-quasi-alternating links, Math. Res. Lett. 17 (2010) 39 MR2592726
12	M Hedden, P Ording, The Ozsváth–Szabó and Rasmussen concordance invariants are not equal, Amer. J. Math. 130 (2008) 441 MR2405163
13	J Hoste, M Thistlethwaite, Knotscape (1999)
14	F Jaeger, A new invariant of plane bipartite cubic graphs, Discrete Math. 101 (1992) 149 MR1172374
15	T C Jaeger, Khovanov–Rozansky homology and Conway mutation (2011) arXiv:1101.3302
16	V F R Jones, Planar algebras, I (1998) arXiv:math/9909027
17	T Kawamura, The Rasmussen invariants and the sharper slice-Bennequin inequality on knots, Topology 46 (2007) 29 MR2288725
18	M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359
19	M Khovanov, A functor-valued invariant of tangles, Algebr. Geom. Topol. 2 (2002) 665 MR1928174
20	M Khovanov, Patterns in knot cohomology, I, Experiment. Math. 12 (2003) 365 MR2034399
21	M Khovanov, $\mathrm{sl}(3)$ link homology, Algebr. Geom. Topol. 4 (2004) 1045
22	M Khovanov, Triply-graded link homology and Hochschild homology of Soergel bimodules, Internat. J. Math. 18 (2007) 869 MR2339573
23	M Khovanov, L Rozansky, Matrix factorizations and link homology, Fund. Math. 199 (2008) 1 MR2391017
24	M Khovanov, L Rozansky, Matrix factorizations and link homology, II, Geom. Topol. 12 (2008) 1387 MR2421131
25	G Kuperberg, Spiders for rank $2$ Lie algebras, Comm. Math. Phys. 180 (1996) 109 MR1403861
26	L Lewark, FoamHo (2012)
27	L Lewark, Rasmussen's spectral sequences and the $\mathfrak{sl}_n$–concordance invariants, in preparation (2013)
28	C Livingston, Computations of the Ozsváth–Szabó knot concordance invariant, Geom. Topol. 8 (2004) 735 MR2057779
29	A Lobb, A slice genus lower bound from $\mathrm{sl}(n)$ Khovanov–Rozansky homology, Adv. Math. 222 (2009) 1220 MR2554935
30	A Lobb, Computable bounds for Rasmussen's concordance invariant, Compos. Math. 147 (2011) 661 MR2776617
31	A Lobb, A note on Gornik's perturbation of Khovanov–Rozansky homology, Algebr. Geom. Topol. 12 (2012) 293 MR2916277
32	M Mackaay, P Vaz, The universal $\mathrm{sl}_3$–link homology, Algebr. Geom. Topol. 7 (2007) 1135 MR2336253
33	M Mackaay, P Vaz, The reduced HOMFLY-PT homology for the Conway and the Kinoshita–Terasaka knots (2008) arXiv:0812.1957
34	C Manolescu, P Ozsváth, On the Khovanov and knot Floer homologies of quasi-alternating links, from: "Proceedings of Gökova Geometry-Topology Conference 2007" (editors S Akbulut, T Önder, R J Stern), GGT Conference (2008) 60 MR2509750
35	S Morrison, A Nieh, On Khovanov's cobordism theory for $\mathfrak{su}_3$ knot homology, J. Knot Theory Ramifications 17 (2008) 1121 MR2457839
36	, MPIR, version 11.0.0 (2012)
37	P Ozsváth, Z Szabó, Heegaard Floer homology and alternating knots, Geom. Topol. 7 (2003) 225 MR1988285
38	, PARI/GP, version 2.5.3 (2012)
39	J A Rasmussen, Some differentials on Khovanov–Rozansky homology (2006) arXiv:math/0607544
40	J A Rasmussen, Khovanov–Rozansky homology of two-bridge knots and links, Duke Math. J. 136 (2007) 551 MR2309174
41	N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
42	A Shumakovitch, KhoHo (2003)
43	A Shumakovitch, Torsion of the Khovanov homology (2004) arXiv:math/0405474
44	A Shumakovitch, Khovanov homology theories and their applications, from: "Perspectives in analysis, geometry, and topology" (editors I Itenberg, B Jöricke, M Passare), Progr. Math. 296, Springer (2012) 403 MR2884045
45	A Stoimenow, Knot data tables (2012)
46	B Webster, Kr.m2 (2005)
47	B Webster, Khovanov–Rozansky homology via a canopolis formalism, Algebr. Geom. Topol. 7 (2007) 673 MR2308960
48	H Wu, The Khovanov–Rozansky cohomology and Bennequin inequalities (2007) arXiv:math/0703210