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 we obtain a spectral sequence converging into . 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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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1980-0549156-2

Keywords:
Principal cofiber bundle,
twisted tensor product,
twisted free tensor product

Article copyright:
© Copyright 1980
American Mathematical Society