A chain coalgebra model for the James map
| dc.creator | Hess, Kathryn | |
| dc.creator | Parent, Paul-Eugene | |
| dc.creator | Scott, Jonathan | |
| dc.date | 2006-09-15 | |
| dc.date.accessioned | 2026-07-07T07:24:52Z | |
| dc.date.available | 2026-07-07T07:24:52Z | |
| dc.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. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0609444 | |
| dc.identifier | http://arxiv.org/abs/math/0609444 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116533 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P35; 55P40 | |
| dc.title | A chain coalgebra model for the James map | |
| dc.type | text |