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.
@article{WBLN_2014__1__A1_0, author = {Audoux, Benjamin}, title = {The {Rasmussen} invariant and the {Milnor} conjecture}, booktitle = {Winter Braids IV (Dijon, 2014)}, series = {Winter Braids Lecture Notes}, note = {talk:1}, pages = {1--19}, publisher = {Winter Braids School}, year = {2014}, doi = {10.5802/wbln.2}, mrnumber = {3703248}, zbl = {1422.57031}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/wbln.2/} }
TY - JOUR AU - Audoux, Benjamin TI - The Rasmussen invariant and the Milnor conjecture BT - Winter Braids IV (Dijon, 2014) AU - Collectif T3 - Winter Braids Lecture Notes N1 - talk:1 PY - 2014 SP - 1 EP - 19 PB - Winter Braids School UR - http://archive.numdam.org/articles/10.5802/wbln.2/ DO - 10.5802/wbln.2 LA - en ID - WBLN_2014__1__A1_0 ER -
%0 Journal Article %A Audoux, Benjamin %T The Rasmussen invariant and the Milnor conjecture %B Winter Braids IV (Dijon, 2014) %A Collectif %S Winter Braids Lecture Notes %Z talk:1 %D 2014 %P 1-19 %I Winter Braids School %U http://archive.numdam.org/articles/10.5802/wbln.2/ %R 10.5802/wbln.2 %G en %F WBLN_2014__1__A1_0
Audoux, Benjamin. The Rasmussen invariant and the Milnor conjecture, dans Winter Braids IV (Dijon, 2014), Winter Braids Lecture Notes (2014), Exposé no. 1, 19 p. doi : 10.5802/wbln.2. http://archive.numdam.org/articles/10.5802/wbln.2/
[1] Computations of Heegaard-Floer knot homology, J. Knot Theory Ramifications, Volume 21 (2012) no. 8, 1250075, 65 pages | MR | Zbl
[2] On Khovanov’s categorification of the Jones polynomial, Algebr. Geom. Topol., Volume 2 (2002), pp. 337-370 | DOI | MR | Zbl
[3] An oriented model for Khovanov homology, J. Knot Theory Ramifications, Volume 19 (2010) no. 2, pp. 291-312 | DOI | MR | Zbl
[4] 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] tangle homology with a parameter and singular cobordisms, Algebr. Geom. Topol., Volume 8 (2008) no. 2, pp. 729-756 | DOI | MR | Zbl
[6] 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] You could have invented spectral sequences, Notices Amer. Math. Soc., Volume 53 (2006) no. 1, pp. 15-19 | MR | Zbl
[8] Fixing the functoriality of Khovanov homology, Geom. Topol., Volume 13 (2009) no. 3, pp. 1499-1582 | DOI | MR | Zbl
[9] Knot Floer homology detects genus-one fibred knots, Am. J. Math., Volume 130 (2008) no. 5, pp. 1151-1169 | DOI | MR | Zbl
[10] An invariant of link cobordisms from Khovanov’s homology theory, Algebr. Geom. Topol (2004), pp. 1211-1251 | DOI | MR | Zbl
[11] Descriptions on surfaces in four space. I. Normal forms., Math. Semin. Notes, Kobe Univ., Volume 10 (1982), pp. 75-126 | MR | Zbl
[12] A categorification of the Jones polynomial, Duke Math. J., Volume 101 (2000) no. 3, pp. 359-426 | MR | Zbl
[13] Gauge theory for embedded surfaces. I., Topology, Volume 32 (1993) no. 4, pp. 773-826 | DOI | MR | Zbl
[14] Khovanov homology is an unknot-detector, Publ. Math., Inst. Hautes Étud. Sci., Volume 113 (2011), pp. 97-208 | DOI | Numdam | MR | Zbl
[15] An endomorphism of the Khovanov invariant, Adv. Math., Volume 197 (2005) no. 2, pp. 554-586 | MR | Zbl
[16] A user’s guide to spectral sequences. 2nd ed., Cambridge: Cambridge University Press, 2001, xv + 561 pages | Zbl
[17] 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] On a certain numerical invariant of link types, Trans. Am. Math. Soc., Volume 117 (1965), pp. 387-422 | DOI | MR | Zbl
[19] Knot Floer homology detects fibred knots, Invent. Math., Volume 170 (2007) no. 3, pp. 577-608 | DOI | MR | Zbl
[20] Erratum: Knot Floer homology detects fibred knots, Invent. Math., Volume 177 (2009) no. 1, pp. 235-238 | DOI | MR | Zbl
[21] Holomorphic disks and genus bounds, Geom. Topol., Volume 8 (2004), pp. 311-334 | DOI | MR | Zbl
[22] Holomorphic disks and knot invariants, Adv. Math., Volume 186 (2004) no. 1, pp. 58-116 | DOI | MR | Zbl
[23] Floer homology and knot complements, Harvard University (2003) (Ph. D. Thesis)
[24] Khovanov homology and the slice genus, Invent. Math., Volume 182 (2010) no. 2, pp. 419-447 | DOI | MR | Zbl
[25] Einführung in die kombinatorische Topologie, Wissenschaftliche Buchgesellschaft, Darmstadt, 1972, xii+209 pages (Unveränderter reprografischer Nachdruck der Ausgabe Braunschweig 1951) | MR | Zbl
[26] Five lectures on Khovanov homology, arXiv:0606464, 2006 | Zbl
[27] A hitchhiker’s guide to Khovanov homology, arXiv:1409.6442, 2014 | Zbl
[28] A method for unknotting torus knots, arXiv:1207.4918, 2012
[29] Khovanov homology, its definitions and ramifications, Fund. Math., Volume 184 (2004), pp. 317-342 | DOI | MR | Zbl
[30] Knots with identical Khovanov homology, Algebr. Geom. Topol., Volume 7 (2007), pp. 1389-1407 | DOI | MR | Zbl
[31] An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38, Cambridge University Press, Cambridge, 1994 | MR | Zbl
Cité par Sources :