A chain coalgebra model for the James map

dc.creatorHess, Kathryn
dc.creatorParent, Paul-Eugene
dc.creatorScott, Jonathan
dc.date2006-09-15
dc.date.accessioned2026-07-07T07:24:52Z
dc.date.available2026-07-07T07:24:52Z
dc.descriptionLet 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.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0609444
dc.identifierhttp://arxiv.org/abs/math/0609444
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116533
dc.subjectAlgebraic Topology
dc.subject55P35; 55P40
dc.titleA chain coalgebra model for the James map
dc.typetext

Files

Collections