Abstract
Let A›tC be a twisted tensor product of an algebra A and a coalgebra C, along a twisting cochain t : C ! A. By means of what is called the tensor trick and under some nice conditions, Gugenheim, Lambe and Stashe proved in the early 90s that A ›t C is homology equivalent to the objects M ›t0 C and A›t00 N, where M and N are strong deformation retracts of A and C, respectively. In this paper, we attack this problem from the point of view of contractions. We find explicit contractions from A ›t C to M ›t0 C and A ›t00 N. Applications to the comparison of resolutions which split o of the bar resolution, as well as to some homological models for central extensions are given.
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