Szczarba’s twisting cochain and the Eilenberg–Zilber maps

• Franz, Matthias ^[1]
  1. [1] University of Western Ontario

     University of Western Ontario

     Canadá

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 72, Fasc. 3, 2021, págs. 569-586
• Idioma: inglés
• DOI: 10.1007/s13348-020-00299-x
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• Resumen

  • 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.