Twisted free tensor products

Katz, Elyahu

doi:10.1090/S0002-9947-1980-0549156-2

Twisted free tensor products
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by Elyahu Katz PDF

Trans. Amer. Math. Soc. 257 (1980), 91-103 Request permission

Abstract:

A twisted free tensor product of a differential algebra and a free differential algebra is introduced. This complex is proved to be chain homotopy equivalent to the complex associated with a twisted free product of a simplicial group and a free simplicial group. In this way we turn a geometric situation into an algebraic one, i.e. for the cofibration $Y \to Y { \cup _g} CX \to \Sigma X$ we obtain a spectral sequence converging into $H(\Omega (Y { \cup _g} CX))$. The spectral sequence obtained in the above situation is similar to the one obtained by L. Smith for a cofibration. However, the one we obtain has more information in the sense that differentials can be traced, requires more lax connectivity conditions and does not need the ring of coefficients to be a field.

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