The Rasmussen invariant and the Milnor conjecture
Benjamin Audoux1
1 Aix Marseille Université, I2M, UMR 7373, 13453 Marseille, France
Winter Braids Lecture Notes, Volume 1 (2014), Talk no. 1, 19 p.

These notes were written for a series of lectures on the Rasmussen invariant and the Milnor conjecture, given at Winter Braids IV in February 2014.

Published online:
DOI: 10.5802/wbln.2
Benjamin Audoux 1

1 Aix Marseille Université, I2M, UMR 7373, 13453 Marseille, France 
@article{WBLN_2014__1__A1_0,
     author = {Benjamin Audoux},
     title = {The {Rasmussen} invariant and the {Milnor} conjecture},
     journal = {Winter Braids Lecture Notes},
     note = {talk:1},
     publisher = {Winter Braids School},
     volume = {1},
     year = {2014},
     doi = {10.5802/wbln.2},
     mrnumber = {3703248},
     zbl = {1422.57031},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/wbln.2/}
}
TY  - JOUR
AU  - Benjamin Audoux
TI  - The Rasmussen invariant and the Milnor conjecture
JO  - Winter Braids Lecture Notes
N1  - talk:1
PY  - 2014
VL  - 1
PB  - Winter Braids School
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/wbln.2/
DO  - 10.5802/wbln.2
LA  - en
ID  - WBLN_2014__1__A1_0
ER  - 
%0 Journal Article
%A Benjamin Audoux
%T The Rasmussen invariant and the Milnor conjecture
%J Winter Braids Lecture Notes
%Z talk:1
%D 2014
%V 1
%I Winter Braids School
%U https://proceedings.centre-mersenne.org/articles/10.5802/wbln.2/
%R 10.5802/wbln.2
%G en
%F WBLN_2014__1__A1_0
Benjamin Audoux. The Rasmussen invariant and the Milnor conjecture. Winter Braids Lecture Notes, Volume 1 (2014), Talk no. 1, 19 p. doi : 10.5802/wbln.2. https://proceedings.centre-mersenne.org/articles/10.5802/wbln.2/

[1] John A. Baldwin; William D. Gillam Computations of Heegaard-Floer knot homology, J. Knot Theory Ramifications, Volume 21 (2012) no. 8, 1250075, 65 pages | MR | Zbl

[2] Dror Bar-Natan On Khovanov’s categorification of the Jones polynomial, Algebr. Geom. Topol., Volume 2 (2002), pp. 337-370 | DOI | MR | Zbl

[3] Christian Blanchet An oriented model for Khovanov homology, J. Knot Theory Ramifications, Volume 19 (2010) no. 2, pp. 291-312 | DOI | MR | Zbl

[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 | Zbl

[5] Carmen Livia Caprau sl(2) tangle homology with a parameter and singular cobordisms, Algebr. Geom. Topol., Volume 8 (2008) no. 2, pp. 729-756 | DOI | MR | Zbl

[6] J.Scott Carter; Masahico Saito Reidemeister moves for surface isotopies and their interpretation as moves to movies., J. Knot Theory Ramifications, Volume 2 (1993) no. 3, pp. 251-284 | DOI | MR | Zbl

[7] Timothy Chow You could have invented spectral sequences, Notices Amer. Math. Soc., Volume 53 (2006) no. 1, pp. 15-19 | MR | Zbl

[8] David Clark; Scott Morrison; Kevin Walker Fixing the functoriality of Khovanov homology, Geom. Topol., Volume 13 (2009) no. 3, pp. 1499-1582 | DOI | MR | Zbl

[9] Paolo Ghiggini Knot Floer homology detects genus-one fibred knots, Am. J. Math., Volume 130 (2008) no. 5, pp. 1151-1169 | DOI | MR | Zbl

[10] Magnus Jacobsson An invariant of link cobordisms from Khovanov’s homology theory, Algebr. Geom. Topol (2004), pp. 1211-1251 | DOI | MR | Zbl

[11] A. Kawauchi; T Shibuya; S. Suzuki Descriptions on surfaces in four space. I. Normal forms., Math. Semin. Notes, Kobe Univ., Volume 10 (1982), pp. 75-126 | MR | Zbl

[12] Mikhail Khovanov A categorification of the Jones polynomial, Duke Math. J., Volume 101 (2000) no. 3, pp. 359-426 | MR | Zbl

[13] Peter B. Kronheimer; Tomasz S. Mrowka Gauge theory for embedded surfaces. I., Topology, Volume 32 (1993) no. 4, pp. 773-826 | DOI | MR | Zbl

[14] Peter B. Kronheimer; Tomasz S. Mrowka Khovanov homology is an unknot-detector, Publ. Math., Inst. Hautes Étud. Sci., Volume 113 (2011), pp. 97-208 | DOI | Numdam | MR | Zbl

[15] Eun Soo Lee An endomorphism of the Khovanov invariant, Adv. Math., Volume 197 (2005) no. 2, pp. 554-586 | MR | Zbl

[16] John McCleary A user’s guide to spectral sequences. 2nd ed., Cambridge: Cambridge University Press, 2001, xv + 561 pages | Zbl

[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 | Zbl

[18] Kunio Murasugi On a certain numerical invariant of link types, Trans. Am. Math. Soc., Volume 117 (1965), pp. 387-422 | DOI | MR | Zbl

[19] Yi Ni Knot Floer homology detects fibred knots, Invent. Math., Volume 170 (2007) no. 3, pp. 577-608 | DOI | MR | Zbl

[20] Yi Ni Erratum: Knot Floer homology detects fibred knots, Invent. Math., Volume 177 (2009) no. 1, pp. 235-238 | DOI | MR | Zbl

[21] Peter Ozsváth; Zoltán Szabó Holomorphic disks and genus bounds, Geom. Topol., Volume 8 (2004), pp. 311-334 | DOI | MR | Zbl

[22] Peter Ozsváth; Zoltán Szabó Holomorphic disks and knot invariants, Adv. Math., Volume 186 (2004) no. 1, pp. 58-116 | DOI | MR | Zbl

[23] Jacob Rasmussen Floer homology and knot complements, Harvard University (2003) (Ph. D. Thesis)

[24] Jacob Rasmussen Khovanov homology and the slice genus, Invent. Math., Volume 182 (2010) no. 2, pp. 419-447 | DOI | MR | Zbl

[25] Kurt Reidemeister Einführung in die kombinatorische Topologie, Wissenschaftliche Buchgesellschaft, Darmstadt, 1972, xii+209 pages (Unveränderter reprografischer Nachdruck der Ausgabe Braunschweig 1951) | MR | Zbl

[26] Paul Turner Five lectures on Khovanov homology, arXiv:0606464, 2006 | Zbl

[27] Paul Turner A hitchhiker’s guide to Khovanov homology, arXiv:1409.6442, 2014 | Zbl

[28] Siwach Vikash; Prabhakar Madeti A method for unknotting torus knots, arXiv:1207.4918, 2012

[29] Oleg Viro Khovanov homology, its definitions and ramifications, Fund. Math., Volume 184 (2004), pp. 317-342 | DOI | MR | Zbl

[30] Liam Watson Knots with identical Khovanov homology, Algebr. Geom. Topol., Volume 7 (2007), pp. 1389-1407 | DOI | MR | Zbl

[31] Charles A. Weibel An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38, Cambridge University Press, Cambridge, 1994 | MR | Zbl

Cited by Sources: