Szczarba's twisting cochain and the Eilenberg-Zilber maps
arXiv:2006.02819 · doi:10.1007/s13348-020-00299-x
Abstract
We show that Szczarba's twisting cochain for a twisted Cartesian product is essentially the same as the one constructed by Shih. More precisely, Szczarba's twisting cochain can be obtained via the basic perturbation lemma if one uses a 'reversed' version of the classical Eilenberg-MacLane homotopy for the Eilenberg-Zilber contraction. Along the way we prove several new identities involving these homotopies.
17 pages; Section 5 revised