2020/08/20 by Matthias Franz, Franz, Matthias · 1 citation
Mathematics · #55R20 #55T10 (Secondary) #55U10 (Primary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2008.08943
openalex publication_date 2020/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the Kan loop group of X is a quasi-isomorphism of dg bialgebras. We also show that Szczarba's twisted shuffle map is a dgc map connecting a twisted Cartesian product with the associated twisted tensor product. This gives a natural dgc model for fibre bundles. We apply our results to finite covering spaces and to the Serre spectral sequence.