Enseignement 2014-2015, semestre 2

M2: Variétés de petite dimension, homologie de Heegaard-Floer


Le cours a lieu le mercredi 13h30-15h30, salle SG-2015, et le vendredi 13h30-15h30, salle ODG-265. Emploi du temps.

Présentation: partie I , partie II .



Résumés du cours et liens sur les articles en référence, partie I (coquilles, omissions ou erreurs possibles; remarques bienvenues !)

Ch1: Exemples de variétés de dimension 3 et 4 (mise à jour 19/02/2015)


• Smale, Diffeomorphisms of the 2-sphere


Ch2: Décomposition en anses, cobordisme (mise à jour 19/02/2015)


• René Thom, Quelques propriétés globales des variétés différentiables Commentarii mathematici Helvetici (1954), Vol 28, pages 17-86.


Ch3: Théorie des noeuds (mise à jour 14/02/2015)


• J. W. Alexander. Topological invariants of knots and links . Trans. Amer. Math. Soc. 30 (1928) 275-306.
• Louis Kauffman. The Conway polynomial. Topology Volume 20, Issue 1, 1981, Pages 101–108
• Louis Kauffman. Sate model and the Jones polynomial. Topology Volume 26, Issue 3, 1987, Pages 395-407


Ch4: Calcul de Kirby et applications


• 1978: R. Kirby, "A Calculus for Framed Links in S3", Inventiones Mathematicae, vol. 45, 35-56.
• 1979: R. P. Fenn and C. P. Rourke, "On Kirby's calculus of links", Topology, vol. 18, 1-15.
• 1997: J. Roberts, "Kirby calculus in manifolds with boundary", Turkish J. Math. 21, no. 1, 111-117
• C. Blanchet, N. Habegger, G. Masbaum, P. Vogel, Three-manifold invariants derived from the Kauffman bracket, Topology 31 (1992), 685-699.


Lecture notes, references, Part II (apologies for errors or typos, remarks more than welcome)

Ch1: Grid diagrams and combinatorial Heegaard-Floer knot homology(upgrade 16/03/2015)


• Dynnikov, Arc-presentations of links: monotonic simplification. Fund. Math. 190 (2006), 29–76.
• Manolescu, Oszvath, Szabo, Thurston D. , On combinatorial link Floer homology, Geometry and Topology, Vol. 12 (2007), 2339-2412.
• Manolescu, Ozsvath, Sarkar, A combinatorial description of knot Floer homology, Annals of Mathematics, Vol. 169 (2009), 633-660


Ch2: Topology of symmetric products


• Kallel, Salvatore, Symmetric products of two dimensional complexes, Contemporary Mathematics Volume 407, 2006.
• Macdonald, Symmetric products of an algebraic curve, Topology. Vol. 1, pp. 319-343 (1962).
• Ozsvath, Peter; Szabó, Zoltán Holomorphic disks and topological invariants for closed three-manifolds. Ann. of Math. (2) 159 (2004), no. 3, 1027–1158.


Ch3: Definition of Heegaard-Floer complexes


• Introduction to Heegaard Floer homology
• Lipshitz, Robert A cylindrical reformulation of Heegaard Floer homology. Geom. Topol. 10 (2006), 955–1097
• Lipshitz, Robert Correction to the article: A cylindrical reformulation of Heegaard Floer homology [MR2240908]. Geom. Topol. 18 (2014), no. 1, 17–30.


Ch4: Holomorphic triangles


• Ozsvath, Peter; Szabó, Zoltán Holomorphic disks and topological invariants for closed three-manifolds. Ann. of Math. (2) 159 (2004), no. 3, 1027–1158.
• Ozsváth, Peter; Szabó, Zoltán Holomorphic disks and three-manifold invariants: properties and applications. Ann. of Math. (2) 159 (2004), no. 3, 1159–1245.
• Lectures on Heegaard Floer homology
• Ozsváth, Peter; Szabó, Zoltán Holomorphic triangles and invariants for smooth four-manifolds. Adv. Math. 202 (2006), no. 2, 326–400.
• Sarkar, Sucharit Maslov index formulas for Whitney n-gons. J. Symplectic Geom. 9 (2011), no. 2, 251–270.


Ch5: Heegaard-Floer homology for knots


• Introduction to Heegaard Floer homology
• Ozsváth, Peter; Szabó, Zoltán Holomorphic disks and knot invariants. Adv. Math. 186 (2004), no. 1, 58–116.

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M2: Topologie algébrique I

MI4: Groupes et arithmétique

Enseignement 2011-2012

M2: Topologie algébrique I et II

M1 Algèbre

Enseignement 2010-2011

M2: Noeuds, tresses et théories d'homologie

M1 Algèbre

M1MME Algorithmique

Enseignement 2009-2010

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