Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Twisted free tensor products

Author: Elyahu Katz
Journal: Trans. Amer. Math. Soc. 257 (1980), 91-103
MSC: Primary 55R99; Secondary 55U10
MathSciNet review: 549156
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55R99, 55U10

Retrieve articles in all journals with MSC: 55R99, 55U10

Additional Information

Keywords: Principal cofiber bundle, twisted tensor product, twisted free tensor product
Article copyright: © Copyright 1980 American Mathematical Society