In this work we show that for any topological space having the homotopy type of a CW-complex and for any commutative ring , the singular cohomology is a Gerstenhaber algebra (see. [7]). In fact we prove that satisfies the conditions of a generalization of the Gerstenhaber algebras.
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Naoufel Battikh 1
@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}, }
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] Gauge algebra and quantization, Phys. Lett., B, Volume 102 (1981) no. 1, pp. 27-31 | DOI | MR
[2] Cup -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] Structures of Gerstenhaber–Voronov algebra on non-commutuative differential forms, Rend. Semin. Mat. Univ. Padova, Volume 141 (2019), pp. 165-183 | DOI | Zbl
[4] Homology operations and loop spaces, Ill. J. Math., Volume 4 (1960), pp. 347-357 | MR | Zbl
[5] Noncommutative differential geometry, Publ. Math., Inst. Hautes Étud. Sci., Volume 62 (1985), pp. 41-144 | DOI | Zbl
[6] 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] The cohomology structure of an associative ring, Ann. Math., Volume 78 (1963), pp. 267-288 | DOI | MR | Zbl
[8] Homotopy theory. An introduction to algebraic topology, Pure and Applied Mathematics, 64, Academic Press Inc., 1975 | Zbl
[9] Formes différentielles non commutatives et cohomologie à coefficients arbitraires, Trans. Am. Math. Soc., Volume 347 (1995) no. 11, pp. 4277-4299 | Zbl
[10] 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] Gerstenhaber and Batalin–Vilkovsky algebras, Arch. Math., Brno, Volume 45 (2009) no. 4, pp. 301-324 | Zbl
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