Forum of Mathematics, Sigma (Jan 2024)

Adams’ cobar construction as a monoidal $E_{\infty }$ -coalgebra model of the based loop space

  • Anibal M. Medina-Mardones,
  • Manuel Rivera

DOI
https://doi.org/10.1017/fms.2024.50
Journal volume & issue
Vol. 12

Abstract

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We prove that the classical map comparing Adams’ cobar construction on the singular chains of a pointed space and the singular cubical chains on its based loop space is a quasi-isomorphism preserving explicitly defined monoidal $E_\infty $ -coalgebra structures. This contribution extends to its ultimate conclusion a result of Baues, stating that Adams’ map preserves monoidal coalgebra structures.

Keywords