Generalized homologies for 𝑑^{𝑁}=0 and graded π‘ž-differential algebras

Author(s):  
Michel Dubois-Violette
2002 β—½  
Vol 9 (3) β—½  
pp. 549-566
Author(s):  
Z. Kharebava

Abstract In the category of differential algebras with strong homotopy there is a Gugenheim's map {ρ 𝑖} : 𝐴* β†’ 𝐢* from Sullivan's commutative cochain complex to the singular cochain complex of a space, which induces a differential graded coalgebra map of appropriate Bar constructions. Both (𝐡𝐴*, dBA , Ξ”,) and (𝐡𝐢*, dBC* , Ξ”,) carry multiplications. We show that the Gugenheim's map 𝐡{ρ 𝑖} : (𝐡𝐴*, dBA* , Ξ”,) β†’ (𝐡𝐢*, dBC* , Ξ”,) is multiplicative up to homotopy with respect to these structures.


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