Total Cofibres of Diagrams of Spectra
| dc.creator | Huettemann, Thomas | |
| dc.date | 2005-08-22 | |
| dc.date.accessioned | 2026-07-07T05:22:34Z | |
| dc.date.available | 2026-07-07T05:22:34Z | |
| dc.description | If Y is a diagram of spectra indexed by an arbitrary poset C together with a specified sub-poset D, we define the total cofibre Γ(Y) of Y as the strict cofibre of the map from hocolim_D (Y) to hocolim_C (Y). We construct a comparison map from the homotopy limit of Y to a looping of a fibrant replacement of Gamma (Y), and characterise those poset pairs (C,D) for which this comparison map is a stable equivalence. The characterisation is given in terms of stable cohomotopy of spaces related to C and D. For example, if C is a finite polytopal complex with underlying space an m-ball with boundary sphere D, then holim_C (Y) and Γ(Y) agree up to m-fold looping and up to stable equivalence. As an application of the general result we give a spectral sequence for the homotopy groups of Γ(Y) with E_2-term involving higher derived inverse limits of π_* (Y), generalising earlier constructions for space-valued diagrams indexed by the face lattice of a polytope. | |
| dc.description | 11 pages; LaTeX source code uses Paul Taylor's "diagrams" and "QED" macro packages; some diagrams may not display correctly with DVI viewers; paper also available at http://nyjm.albany.edu:8000/j/2005/11-16.html | |
| dc.identifier | https://arxiv.org/abs/math/0508406 | |
| dc.identifier | http://arxiv.org/abs/math/0508406 | |
| dc.identifier | New York Journal of Mathematics 11 (2005), pp. 333-343 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76109 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55P99 (Primary) 57Q05 (Secondary) | |
| dc.title | Total Cofibres of Diagrams of Spectra | |
| dc.type | text |