Topologie algébrique

Hector Cordova Bulens
Gery Debongnie
Julien Federinov
Yves Felix
Pascal Lambrechts
Paul Songhafouo Tsopméné

Subjects of Research 

Rational Homotopy, Lusternik-Schnirelmann category, Applications of rational homotopy to problems in geometry (loop space homology, homotopy type and rational homotopy type of configuration spaces, space of embeddings, Chas-Sullivan string topology, elliptic-hyperbolic dichotomy...)

Rational homotopy theory

The book Rational Homotopy Theory and a list of corrections
An introduction text to rational homotopy theory (dvi)
A bibliography of rational homotopy theory. This bibliography, written initially by Professor Bartik and completed in 96 by Yves Félix and Daniel Tanré, contains 2000 references.
The software bigrade. The software has been written (in C) by Steve Halperin and Bernardo Macchiusi and computes the Sullivan minimal model of a commutative graded algebra.

Publications 

• Greg Arone, Pascal Lambrechts and Ismar Volic. Calculus of functors, operad formality, and rational homology of embedding spaces, Acta Mathematica 199 (2007), 153­198, (available on arXiv:math.AT/0607486)
• Félix Y.,   Halperin S., Thomas  J.-C., The ranks of    the homotopy groups of   a space of finite LS category,  Expositiones Math. 25 (2007), 67-76.
•  Greg Arone, Pascal Lambrechts, Victor Turchin, and Ismar Volic. Coformality and rational homotopy groups of spaces of long knots, Math. Res. Lett. 15 (2008), no. 1, 1­14. (available on arXiv:math.AT/0701350)
• Pascal Lambrechts and Don Stanley. Poincaré duality and commutative differential graded algebras, Annales Scientifiques de l'École Normale Supérieure 41 (2008) 495­509 (available on arXiv:math.AT/0701309)
• Pascal Lambrechts and Don Stanley. The rational homotopy type of a blowup in the stable case, Geometry and Topology 12 (2008) 1921­1993 (available on arXiv:0706.1363)
• Pascal Lambrechts and Don Stanley. A remarkable DG-module model for configuration spaces, Algebraic and Geometric Topology 8 (2008) 1191­1222. (available on arXiv:0707.2350)
• Félix Y.,  Oprea J.,  Tanré D.,   Algebraic Models in Geometry, Livre Oxford Graduate Texts in Mathematics, 2008.
• Félix Y.,  Thomas J.-C.,   Rational BV-algebra in string topology, Bull. Soc. Math. France 136 (2008),  311-327.
• Félix Y.,  Tanré D.,   Rational homotopy of the polyhedral product functor, Proc. Amer. Math. Soc. 137 (2009), 891-898.
• Félix Y.,   Oprea J.,   Rational homotopy of gauge groups, Proc. Amer. Math. Soc. 137 (2009), 1519-1527.
• Félix Y.,  Jessup B., Parent  P.-E.,  A proof of the combinatorial model for the Sullivan functor on simplicial sets, Journal of Pure and Applied Algebra 211 (2009), 231-240.
• Félix Y.,   Halperin S.,   Thomas J.C.,  Exponential growth and an asymptotic  formula for the ranks of   homotopy groups of a finite 1-connected complex,  Annals of Mathematics 170 (2009), 387-408.
• Buijs U.,  Félix Y.,  Murillo A.,   Rational homotopy of the fixed and homotopy fixed point sets, Advances in Mathematics 222 (2009), 151-171
• Félix Y., Thomas J.-C.,  String topology on Gorenstein spaces Math. Annalen {\bf 345} (2009), 345-452.
• Buijs U.,  Félix Y.,   Murillo A.,  Lie models for the components of sections of a nilpotent bundle, Trans. Amer. Math. Soc. {\bf 361} (2009) 5601-5614.
• Félix Y.,   Halperin S., Thomas  J.-C.,  The structure of homotopy Lie algebras,   Comment. Math. Helv.  {\bf  84}  (2009), 807–833.
• Pascal Lambrechts and Victor Turchin. Homotopy Graph-complex for configuration and knot spaces, Trans. Amer. Math. Soc. 361 (2009), 207­222 (available on arXiv:math.AT/0611766)

Webpage of the team