The Rasmussen invariant and the Milnor conjecture

 Access to full text

 Full (PDF)

1. John A. Baldwin, William D. Gillam, Computations of Heegaard-Floer knot homology, J. Knot Theory Ramifications 21 (2012) Zbl1288.57010MR2925428
2. Dror Bar-Natan, On Khovanov’s categorification of the Jones polynomial, Algebr. Geom. Topol. 2 (2002), 337-370 Zbl0998.57016MR1917056
3. Christian Blanchet, An oriented model for Khovanov homology, J. Knot Theory Ramifications 19 (2010), 291-312 Zbl1195.57024MR2647055
4. Michel Boileau, Claude Weber, Le problème de J. Milnor sur le nombre gordien des noeuds algébriques, Noeuds, tresses et singularités, C. R. Sémin., Plans-sur-Bex 1982, Monogr. Enseign. Math. 31, 49-98 (1983). (1983) Zbl0556.57001MR728580
5. Carmen Livia Caprau, $\text{sl}\left(2\right)$ tangle homology with a parameter and singular cobordisms, Algebr. Geom. Topol. 8 (2008), 729-756 Zbl1148.57016MR2443094
6. J.Scott Carter, Masahico Saito, Reidemeister moves for surface isotopies and their interpretation as moves to movies., J. Knot Theory Ramifications 2 (1993), 251-284 Zbl0808.57020MR1238875
7. Timothy Chow, You could have invented spectral sequences, Notices Amer. Math. Soc. 53 (2006), 15-19 Zbl1092.55014MR2189946
8. David Clark, Scott Morrison, Kevin Walker, Fixing the functoriality of Khovanov homology, Geom. Topol. 13 (2009), 1499-1582 Zbl1169.57012MR2496052
9. Paolo Ghiggini, Knot Floer homology detects genus-one fibred knots, Am. J. Math. 130 (2008), 1151-1169 Zbl1149.57019MR2450204
10. Magnus Jacobsson, An invariant of link cobordisms from Khovanov’s homology theory, Algebr. Geom. Topol (2004), 1211-1251 Zbl1072.57018MR2113903
11. A. Kawauchi, T Shibuya, S. Suzuki, Descriptions on surfaces in four space. I. Normal forms., Math. Semin. Notes, Kobe Univ. 10 (1982), 75-126 Zbl0506.57014MR672939
12. Mikhail Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000), 359-426 Zbl0960.57005MR1740682
13. Peter B. Kronheimer, Tomasz S. Mrowka, Gauge theory for embedded surfaces. I., Topology 32 (1993), 773-826 Zbl0799.57007
14. Peter B. Kronheimer, Tomasz S. Mrowka, Khovanov homology is an unknot-detector, Publ. Math., Inst. Hautes Étud. Sci. 113 (2011), 97-208 Zbl1241.57017
15. Eun Soo Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005), 554-586 Zbl1080.57015MR2173845
16. John McCleary, A user’s guide to spectral sequences. 2nd ed., (2001), Cambridge: Cambridge University Press Zbl0959.55001MR1793722
17. John W. Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies. 61. Princeton, N.J.: Princeton University Press and the University of Tokyo Press. 122 p. (1968). (1968) Zbl0184.48405
18. Kunio Murasugi, On a certain numerical invariant of link types, Trans. Am. Math. Soc. 117 (1965), 387-422 Zbl0137.17903MR171275
19. Yi Ni, Knot Floer homology detects fibred knots, Invent. Math. 170 (2007), 577-608 Zbl1138.57031MR2357503
20. Yi Ni, Erratum: Knot Floer homology detects fibred knots, Invent. Math. 177 (2009), 235-238 Zbl1162.57300MR2507641
21. Peter Ozsváth, Zoltán Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004), 311-334 Zbl1056.57020
22. Peter Ozsváth, Zoltán Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004), 58-116 Zbl1062.57019
23. Jacob Rasmussen, Floer homology and knot complements, (2003) MR2704683
24. Jacob Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010), 419-447 Zbl1211.57009MR2729272
25. Kurt Reidemeister, Einführung in die kombinatorische Topologie, (1972), Wissenschaftliche Buchgesellschaft, Darmstadt Zbl0042.17702MR345088
26. Paul Turner, Five lectures on Khovanov homology, arXiv:0606464 (2006) 
27. Paul Turner, A hitchhiker’s guide to Khovanov homology, arXiv:1409.6442 (2014) 
28. Siwach Vikash, Prabhakar Madeti, A method for unknotting torus knots, arXiv:1207.4918 (2012) Zbl1270.57034
29. Oleg Viro, Khovanov homology, its definitions and ramifications, Fund. Math. 184 (2004), 317-342 Zbl1078.57013MR2128056
30. Liam Watson, Knots with identical Khovanov homology, Algebr. Geom. Topol. 7 (2007), 1389-1407 Zbl1137.57020MR2350287
31. Charles A. Weibel, An introduction to homological algebra, 38 (1994), Cambridge University Press, Cambridge Zbl0797.18001MR1269324