A chain coalgebra model for the James map

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Let EK be the simplicial suspension of a pointed simplicial set K. We construct a chain model of the James map, $α_{K} : CK \to ΩCEK$. We compute the cobar diagonal on $ΩCEK$, not assuming that $EK$ is 1-reduced, and show that $α_{K}$ is comultiplicative. As a result, the natural isomorphism of chain algebras $TCK \cong ΩCK$ preserves diagonals. In an appendix, we show that the Milgram map, $Ω(A \otimes B) \to ΩA \otimes ΩB$, where A and B are coaugmented coalgebras, forms part of a strong deformation retract of chain complexes. Therefore, it is a chain equivalence even when A and B are not 1-connected.
20 pages

Keywords

Algebraic Topology, 55P35; 55P40

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/116533

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0609444
 http://arxiv.org/abs/math/0609444

Collections

arXiv