Homologie et modèle minimal des algèbres de Gerstenhaber

Ginot, Grégory

Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 1, pp. 95-126.

On étudie ici les notions d’algèbre de Gerstenhaber à homotopie près et d’homologie des algèbres de Gerstenhaber du point de vue de la théorie des opérades. Précisément, on donne une description explicite des $𝒢$-algèbres à homotopie près (c’est-à-dire d’algèbres sur le modèle minimal de l’opérade $𝒢$ des algèbres de Gerstenhaber). On décrit également le complexe calculant l’homologie des $𝒢$-algèbres. On donne une suite spectrale qui converge vers cette homologie et quelques exemples de calculs. Enfin on explicite la structure d’algèbre de Poisson à homotopie près.

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