Benoit Fresse
Professeur des universités
CNU : SECTION 25 - MATHEMATIQUES
Lab(s)
Publications
The surveys of the Zentralblatt für Mathematik (Zbl xxxx.yyzzz) are accessible without subscription. The surveys of the Mathematical Reviews (MR xxxyyyy) are accessible with a subscription to MathSciNet.
Books
- 2017a : Homotopy of operads & Grothendieck-Teichmüller groups, Mathematical Surveys and Monographs 217, American Mathematical Society, 2017. xl+534 pages (first volume), xxxi+704 pages (second volume).
- Publication.
- Book project web page.
- Preprint hal-00656333, 2012, 200 pages. (Excerpts from the book in preparation, and document draft for the course Operads 2012.)
- Reviews Zbl 1373.55014-Zbl 1375.55007 and MR 3643404-MR 3616816.
- 2009a : Modules over operads and functors, Lecture Notes in Mathematics 1967, Springer Verlag, 2009. 318 pages.
- Reviews Zbl 1178.18007 et MR2494775.
Book chapters
- 2019a : Little discs operads, graph complexes and Grothendieck-Teichmüller groups, in "Handbook of Homotopy Theory (Haynes Miller editor)". Handbooks in Mathematics Series, CRC Press/Chapman and Hall (2019), pp. 407-444. Publication. Preprint arXiv:1811.12536 (preliminary version, significantly differs from the final version) and latest manuscript (final version).
Articles
- 2024a : Graph complexes and models of chain En-operads in odd characteristic, in "Homotopical algebra and higher structures (Oberwolfach, 2024)". Oberwolfach reports (2024), en ligne. Publication. Manuscript.
- 2022a, with Julien Ducoulombier and Victor Turchin : Projective and Reedy model category structures for (infinitesimal) bimodules over an operad. Appl. Categ. Structures 30 (2022), pp. 825-920. Publication. Manuscript.
- 2020pre, with Lorenzo Guerra : On a notion of homotopy Segal E-infinity-Hopf cooperad. Prépublication arXiv:2011.11333 (2020). Manuscript.
- 2020pre, with Victor Turchin and Thomas Willwacher : On the rational homotopy type of embedding spaces of manifolds in Rn. Preprint arXiv:2008.08146 (2020). Manuscript.
- 2020pre, with Thomas Willwacher : Mapping spaces for dg Hopf cooperads and homotopy automorphisms of the rationalization of En-operads. Preprint arXiv:2003.02939 (2020). Manuscript.
- 2020a, with Thomas Willwacher : The intrinsic formality of En-operads. J. Eur. Math. Soc. (JEMS) 22 (2020), pp. 2047-2133. Publication. Manuscript. Reviews Zbl 1445.18014 and MR 4107503.
- 2018a : The extended rational homotopy theory of operads. Georgian Math. J. 25 (2018), pp. 493-512. Publication. Manuscript. Reviews Zbl 1408.18017 et MR 3881488.
- 2018b, with Victor Turchin and Thomas Willwacher : The homotopy theory of operad subcategories. J. Homotopy Relat. Struct. 13 (2018), pp. 689-702. Publication. Manuscript. Reviews Zbl 1405.18015 and MR 3870769.
- 2017pre, with Victor Turchin et Thomas Willwacher : The rational homotopy of mapping spaces of En operads. Preprint arXiv:1703.06123 (2017). Manuscript.
- 2016a : The cotriple resolution of differential graded algebras. Proc. Amer. Math. Soc. 144 (2016), pp. 4693-4707. Publication. Manuscript. Reviews Zbl 1366.18007 and MR 3544521.
- 2016b, with Stephanie Ziegenhagen : Iterated bar complexes and En-homology with coefficients. J. Pure Appl. Algebra 220 (2016), pp. 683-710. Publication. Manuscript. Reviews Zbl 1348.57052 and MR 3399385.
- 2014a : 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), pp. 165-188. Publication. Manuscript. Reviews Zbl 1339.55013 and MR 3243398.
- 2013a : La catégorie des arbres élagués de Batanin est de Koszul, in "Opérades 2009 (Luminy, 2009)". Sém. Congrès 26, Soc. Math. Fr. (2013), pp. 99-144. Publication. Manuscript. Reviews Zbl 1277.57030 and MR 2803847.
- 2011a : Koszul duality of En-operads. Selecta Math. 17 (2011), pp. 363-434. Publication. Manuscript. Reviews Zbl 1248.55003 and MR 2803847.
- 2011b : On mapping spaces of differential graded operads with the commutative operad as target. Math. Res. Lett. 18 (2011), pp. 215-230. Publication. Manuscript. Reviews Zbl 1241.55006 and MR 2784668.
- 2011c : Iterated bar complexes of E-infinity algebras and homology theories. Alg. Geom. Topol. 11 (2011), pp. 747-838. Publication. Manuscript. Reviews Zbl 1238.57034 and MR 2782544.
- 2010a : Props in model categories and homotopy invariance of structures. Georgian Math. J. 17 (2010), pp. 79-160. Publication. Manuscript. Reviews Zbl 1227.18007 and MR 2640648.
- 2010b : The bar complex of an E-infinity algebra. Adv. Math. 223 (2010), pp. 2049-2096. Publication. Reviews Zbl 1208.57017 and MR 2601008.
- 2009b : 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), pp. 125-189. Publication. Manuscript. Reviews Zbl 1283.18007 and MR 2581912.
- 2006a : Théorie des opérades de Koszul et homologie des algèbres de Poisson. Ann. Math. Blaise Pascal 13 (2006), pp. 237-312. Publication. Reviews Zbl 1141.55006 and MR2275449 (2009b:17051).
- 2004a : Koszul duality of operads and homology of partition posets, in "Homotopy theory and its applications (Evanston, 2002)", Contemp. Math. 346, Amer. Math. Soc. (2004), pp. 115-215. Publication. Manuscript. Reviews Zbl 1077.18007 and MR2066499 (2005g:18015).
- 2004b, with Clemens Berger : Combinatorial operad actions on cochains. Math. Proc. Cambridge Philos. Soc. 137 (2004), pp. 135-174. Publication. Reviews Zbl 1056.55006 and MR2075046 (2005e:18013).
- 2003a : La construction bar d'une algèbre comme algèbre de Hopf E-infini. C. R. Acad. Sci. Paris Sér. I Math. 337 (2003), pp. 403-408. Publication. Reviews Zbl 1068.57035 and MR 2004h:18008.
- 2002a, with Clemens Berger : Une décomposition prismatique de l'opérade de Barratt-Eccles. C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), pp. 365-370. Publication. Reviews Zbl 1016.18005 and MR 2003m:55006.
- 2002b : Structures de Poisson sur une intersection complète à singularitées isolées. C. R. Acad. Sci. Paris Sér. I Math. 335 (2002), pp. 5-10. Publication. Reviews Zbl 1095.13525 and MR 2003g:13017.
- 2000a : On the homotopy of simplicial algebras over an operad. Trans. Amer. Math. Soc., 352 (2000), pp. 4113-4141. Publication. Reviews Zbl 0958.18005 and MR 2000m:18015.
- 1998a : Algèbre des descentes et cogroupes dans les algèbres sur une opérade. Bull. Soc. Math. Fr. 126 (1998), pp. 407-433. Publication. Reviews Zbl 0940.18004 and MR 2000c:16049.
- 1998b : Cogroups in algebras over an operad are free algebras. Comment. Math. Helv. 73 (1998), pp. 637-676. Publication. Reviews Zbl 0929.16033 and MR 99i:18010.
- 1998c : Homologie de Quillen pour les algèbres de Poisson. C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), pp. 1053-1058. Publication. Reviews Zbl 0922.17014 and MR 99j:16001.
- 1998d : Lie theory of formal groups over an operad. J. of Algebra 202 (1998), pp. 455-511. Publication. Reviews Zbl 1041.18009 and MR 99c:14063.
- 1997a : Opérations de Cartan pour les algèbres simpliciales sur une opérade. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), pp. 247-252. Publication. Reviews Zbl 0981.18011 and MR 98c:18009.
Memoirs
- 2002c : Structures d'opérades en algèbre homologique. Mémoire d'habilitation à diriger des recherches, Université de Nice-Sophia-Antipolis, 2002. 36 pages. Manuscrit.
- 1996a : Cogroupes dans les algèbres sur une opérade. Thèse de Doctorat de l'Université Louis Pasteur (Strasbourg 1), 1996. 107 pages.
Notes and document drafts
- 2014pre : Functor homology and operadic homology. Document draft (2014). Manuscript.
- 2009pre : Le complexe bar itéré des En-algèbres comme un diagramme homotopique sur la catégorie des arbres élagués. Document draft (2009), 67 pages. Manuscript.
- 2008pre : 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. Manuscript.
- 2007pre : The universal Hopf operads of the bar construction. Document draft (2007), 125 pages. Manuscript.
- 2002pre : Derived division functors and mapping spaces. Document draft (2002), 34 pages. Manuscript.
- 1998pre : Homologie de Poisson de surfaces à une singularité isolée. Notes (1998). Manuscript.
- 1997pre Applications polynomiales et foncteurs polynomiaux. Notes of a talk (1997), 24 pages. Manuscript.