Benoit Fresse's home page


Address:
Université de Lille
Laboratoire Paul Painlevé
Cité Scientifique - Bâtiment M2
F-59655 Villeneuve d'Ascq Cedex
Phone: (33) 3 20 43 45 71

E-mail:

Research

Publications

  1. Cogroupes dans les algèbre sur une opérade, Thèse de doctorat de l'Université Louis Pasteur (Strasbourg 1), 1996, 107 pages.
  2. Opérations de Cartan pour les algèbres simpliciales sur une opérade, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 247-252. Publication. Reviews MR 98c:18009 and Zbl 0981.18011.
  3. Lie theory of formal groups over an operad, J. of Algebra 202 (1998), 455-511. Publication. Reviews MR 99c:14063 and Zbl 1041.18009.
  4. Homologie de Quillen pour les algèbres de Poisson, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), 1053-1058. Publication. Reviews MR 99j:16001 and Zbl 0922.17014.
  5. Cogroups in algebras over an operad are free algebras, Comment. Math. Helv. 73 (1998), 637-676. Publication. Reviews MR 99i:18010 and Zbl 0929.16033.
  6. Algèbre des descentes et cogroupes dans les algèbres sur une opérade, Bull. Soc. Math. Fr. 126 (1998), 407-433. Publication. Reviews MR 2000c:16049 and Zbl 0940.18004.
  7. On the homotopy of simplicial algebras over an operad, Trans. Amer. Math. Soc., 352 (2000), 4113-4141. Publication. Reviews MR 2000m:18015 and Zbl 0958.18005.
  8. Structures de Poisson sur une intersection complète à singularitées isolées, C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), 5-10. Publication. Reviews MR 2003g:13017 and Zbl 1095.13525.
  9. Une décomposition prismatique de l'opérade de Barratt-Eccles, with Clemens Berger, C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), 365-370. Publication. Reviews MR 2003m:55006 and Zbl 1016.18005.
  10. La construction bar d'une algèbre comme algèbre de Hopf E-infini, C. R. Acad. Sci. Paris Sér. I Math. 337 (2003), 403-408. Publication. Reviews MR 2004h:18008 and Zbl 1068.57035.
  11. Combinatorial operad actions on cochains, with Clemens Berger, Math. Proc. Cambridge Philos. Soc. 137 (2004), 135-174. Publication. Reviews MR2075046 (2005e:18013) and Zbl 1056.55006.
  12. Koszul duality of operads and homology of partition posets, in "Homotopy theory and its applications (Evanston, 2002)", Contemp. Math. 346, Amer. Math. Soc. (2004), 115-215. Manuscript, Publication. Reviews MR2066499 (2005g:18015) and Zbl 1077.18007.
  13. Théorie des opérades de Koszul et homologie des algèbres de Poisson, Ann. Math. Blaise Pascal 13 (2006), 237-312. Publication. Reviews MR2275449 (2009b:17051) and Zbl 1141.55006.
  14. Modules over operads and functors, Lecture Notes in Mathematics 1967, Springer Verlag, 2009, 318 pages. Manuscript, Publication. Reviews MR2494775 and Zbl 1178.18007.
  15. Operadic cobar constructions, cylinder objects and homotopy morphisms of algebras over operads, in "Alpine perspectives on algebraic topology (Arolla, 2008)", Contemp. Math. 504, Amer. Math. Soc. (2009), 125-189. Manuscript, Publication. Reviews MR 2581912 and Zbl 1283.18007.
  16. The bar complex of an E-infinity algebra, Adv. Math. 223 (2010), pp. 2049-2096. Publication, Reviews MR 2601008 and Zbl 1208.57017.
  17. Props in model categories and homotopy invariance of structures, Georgian Math. J. 17 (2010), pp. 79-160. Manuscript, Publication. Reviews MR 2640648 and Zbl 1227.18007.
  18. Iterated bar complexes of E-infinity algebras and homology theories, Alg. Geom. Topol. 11 (2011), pp. 747-838. Manuscript, Publication. Reviews MR 2782544 and Zbl 1238.57034.
  19. On mapping spaces of differential graded operads with the commutative operad as target, Math. Res. Lett. 18 (2011), pp. 215-230. Manuscript, Publication. Reviews MR 2784668 and Zbl 1241.55006.
  20. Koszul duality of En-operads, Selecta Math. 17 (2011), 363-434. Manuscript, Publication. Reviews MR 2803847 and Zbl 1248.55003. Talk at the 3rd Arolla Topology Conference, Arolla, Switzerland (2008), PDF Presentation.
  21. La catégorie des arbres élagués de Batanin est de Koszul, in"Opérades 2009 (Luminy, 2009)", Sém. Congrès 26, Soc. Math. Fr. (2013), 99-144. Manuscript, Publication. Reviews MR 2803847 and Zbl 1277.57030.
  22. Koszul duality complexes for the cohomology of iterated loop spaces of spheres, in "An Alpine expedition through algebraic topology (Arolla, 2012)", Contemp. Math. 617, Amer. Math. Soc. (2014), 165-188. Manuscript, Publication. Reviews MR 3243398 and Zbl 1339.55013.
  23. Iterated bar complexes and En-homology with coefficients, with Stephanie Ziegenhagen, J. Pure Appl. Algebra 220 (2016), 683-710. Manuscript, Publication. Reviews MR 3399385 and Zbl 1348.57052.
  24. The cotriple resolution of differential graded algebras, Proc. Amer. Math. Soc. 144 (2016), 4693-4707. Manuscript, Publication. Reviews MR 3544521 and Zbl 1366.18007.
  25. Homotopy of operads & Grothendieck-Teichmüller groups, Mathematical Surveys and Monographs, American Mathematical Society, 2017, xl+534 pages (first volume), xxxi+704 pages (second volume).
  26. The homotopy theory of operad subcategories, with Victor Turchin and Thomas Willwacher, J. Homotopy Relat. Struct. 13 (2018), 689-702. Manuscript, Publication.
  27. The extended rational homotopy theory of operads, Georgian Math. J. (2018). Manuscript, Publication.

Preprints

  1. The intrinsic formality of En-operads, with Thomas Willwacher, preprint arXiv:1503.08699 (2015), to appear in J. Eur. Math. Soc. (JEMS). Manuscript.
  2. The rational homotopy of mapping spaces of En operads, with Victor Turchin and Thomas Willwacher, preprint arXiv:1703.06123 (2017). Abstract, Manuscript.
  3. Little discs operads, graph complexes and Grothendieck-Teichmüller groups, preprint arXiv:1811.12536 (2018). Paper in preparation for a new "handbook of homotopy theory" (Haynes Miller editor). Manuscript.

Miscellaneous notes and internal reports

  1. Functor homology and operadic homology, notes (2014). Article draft.
  2. Iterated bar complexes and the poset of pruned trees. Addendum to the paper "Iterated bar complexes of E-infinity algebras and homology theories", notes (2008), 13 pages. Abstract, Addendum.
  3. The universal Hopf operads of the bar construction, memoir to be revised (2007), 125 pages. Abstract, Full text.
  4. Derived division functors and mapping spaces, preprint to be revised (2002), 34 pages. Abstract, Article.
  5. Le complexe bar itéré des En-algèbres comme un diagramme homotopique sur la catégorie des arbres élagués, preprint (2009), 67 pages. Abstract, Article.
  6. Homologie de Poisson de surfaces à une singularité isolée, notes (1998). Article.
  7. Applications polynomiales et foncteurs polynomiaux, notes of a talk (1997), 24 pages. Full text.
  8. Structures d'opérades en algèbre homologique, mémoire d'habilitation à diriger des recherches (2002), 36 pages. Full text.

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(1/11/2018)