English

Szczarba's twisting cochain and the Eilenberg-Zilber maps

Algebraic Topology 2021-08-31 v2

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.

Keywords

Cite

@article{arxiv.2006.02819,
  title  = {Szczarba's twisting cochain and the Eilenberg-Zilber maps},
  author = {Matthias Franz},
  journal= {arXiv preprint arXiv:2006.02819},
  year   = {2021}
}

Comments

17 pages; Section 5 revised