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Transactions of the American Mathematical Society

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Twisted free tensor products

Author: Elyahu Katz
Journal: Trans. Amer. Math. Soc. 257 (1980), 91-103
MSC: Primary 55R99; Secondary 55U10
MathSciNet review: 549156
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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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Keywords: Principal cofiber bundle, twisted tensor product, twisted free tensor product
Article copyright: © Copyright 1980 American Mathematical Society

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