Journal
COLLECTANEA MATHEMATICA
Volume 72, Issue 3, Pages 569-586Publisher
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s13348-020-00299-x
Keywords
Twisted Cartesian product; Szczarba's twisting cochain; Shih's twisting cochain; Eilenberg-Zilber maps; Basic perturbation lemma
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Funding
- NSERC Discovery Grant
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Our research demonstrates that Szczarba's twisting cochain for a twisted Cartesian product is essentially equivalent to the one created by Shih. Specifically, by utilizing a 'reversed' version of the classical Eilenberg-Mac Lane homotopy for the Eilenberg-Zilber contraction, Szczarba's twisting cochain can be derived via the basic perturbation lemma. Along the way, we establish several new identities involving these homotopies.
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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