Szczarba’s twisting cochain and the Eilenberg–Zilber maps
Collectanea Mathematica(2021)
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–Mac Lane homotopy for the Eilenberg–Zilber contraction. Along the way we prove several new identities involving these homotopies.
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Key words
Twisted Cartesian product,Szczarba’s twisting cochain,Shih’s twisting cochain,Eilenberg-Zilber maps,Basic perturbation lemma,Primary 55U10,Secondary 55R20,55U25
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