A cubical model for a fibration

Abstract

In the paper the notion of truncating twisting function $\tau :X\to Q$ from a simplicial set $X$ to a cubical set $Q$ and the corresponding notion of twisted Cartesian product of these sets $X{\times }_{\tau }Q$ are introduced. The latter becomes a cubical set whose chain complex coincides with the standard twisted tensor product $C_{\ast }(X){\otimes }_{{\tau }_{\ast }}{C}_{\ast }(Q)$. This construction together with the theory of twisted tensor products for homotopy G-algebras allows to obtain multiplicative models for fibrations.

15 pages, 1 figure