Comptes Rendus
Algèbre
Formes différentielles non commutatives et Algèbres de Gerstenhaber
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 31-44.

In this work we show that for any topological space X having the homotopy type of a CW-complex and for any commutative ring R, the singular cohomology H * (X;R) is a Gerstenhaber algebra (see. [7]). In fact we prove that H * (X;R) satisfies the conditions of a generalization of the Gerstenhaber algebras.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.386
Classification : 17D99, 55N10

Naoufel Battikh 1

1 Département des mathématiques, UFR des sciences, Université de Versailles-Saint-Quentin, France.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2023__361_G1_31_0,
     author = {Naoufel Battikh},
     title = {Formes diff\'erentielles non commutatives et {Alg\`ebres} de {Gerstenhaber}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {31--44},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.386},
     language = {fr},
}
TY  - JOUR
AU  - Naoufel Battikh
TI  - Formes différentielles non commutatives et Algèbres de Gerstenhaber
JO  - Comptes Rendus. Mathématique
PY  - 2023
SP  - 31
EP  - 44
VL  - 361
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.386
LA  - fr
ID  - CRMATH_2023__361_G1_31_0
ER  - 
%0 Journal Article
%A Naoufel Battikh
%T Formes différentielles non commutatives et Algèbres de Gerstenhaber
%J Comptes Rendus. Mathématique
%D 2023
%P 31-44
%V 361
%I Académie des sciences, Paris
%R 10.5802/crmath.386
%G fr
%F CRMATH_2023__361_G1_31_0
Naoufel Battikh. Formes différentielles non commutatives et Algèbres de Gerstenhaber. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 31-44. doi : 10.5802/crmath.386. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.386/

[1] G. A. Batalin Gauge algebra and quantization, Phys. Lett., B, Volume 102 (1981) no. 1, pp. 27-31 | DOI | MR

[2] Naoufel Battikh Cup i-produits sur les formes différentielles non commutatives et carrés de Steenrod, J. Algebra, Volume 313 (2007) no. 2, pp. 531-553 | DOI | MR | Zbl

[3] Naoufel Battikh; Hatem Issaoui Structures of Gerstenhaber–Voronov algebra on non-commutuative differential forms, Rend. Semin. Mat. Univ. Padova, Volume 141 (2019), pp. 165-183 | DOI | Zbl

[4] William Browder Homology operations and loop spaces, Ill. J. Math., Volume 4 (1960), pp. 347-357 | MR | Zbl

[5] Alain Connes Noncommutative differential geometry, Publ. Math., Inst. Hautes Étud. Sci., Volume 62 (1985), pp. 41-144 | DOI | Zbl

[6] Albrecht Dold; René Thom Une généralisation de la notion d’espace fibré. Application aux produits symétriques infinis, C. R. Math. Acad. Sci. Paris, Volume 242 (1956), pp. 1680-1682 | Zbl

[7] Murray Gerstenhaber The cohomology structure of an associative ring, Ann. Math., Volume 78 (1963), pp. 267-288 | DOI | MR | Zbl

[8] Brayton Gray Homotopy theory. An introduction to algebraic topology, Pure and Applied Mathematics, 64, Academic Press Inc., 1975 | Zbl

[9] Max Karoubi Formes différentielles non commutatives et cohomologie à coefficients arbitraires, Trans. Am. Math. Soc., Volume 347 (1995) no. 11, pp. 4277-4299 | Zbl

[10] J. Peter May A general algebraic approach to Steenrod operations, The Steenrod Algebra and its Applications (Lecture Notes in Mathematics), Volume 168, Springer (1970), pp. 153-231 | MR

[11] Claude Roger Gerstenhaber and Batalin–Vilkovsky algebras, Arch. Math., Brno, Volume 45 (2009) no. 4, pp. 301-324 | Zbl

Cité par Sources :

Commentaires - Politique