Shuffle groups and brace Algebra in Algebraic topology and combinatorics: Operads

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In this thesis, we use operad theory to develop some constructions that provide to any pointed multiplicative operads some Algebraic structures as: cosimplicial structure, bicomplex structure, bicomplex Algebra structure, A_\infty-algebra structure. Moreover, to show that our results are naturals, WE apply them on particular exemples where we observe that, our results clarify, coïncide, extend some well-known results in the litterature and subsequently our constructions allow us to go further. Secondly, we study the fine structure of the cohomology comparison theorem of Gerstenhaber and Schack, where we extend the theorem in different algebraic frames as: coalgebra, cosimplicial, brace Algebra, operad.

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