James bundles
| dc.creator | Fenn, Roger | |
| dc.creator | Rourke, Colin | |
| dc.creator | Sanderson, Brian | |
| dc.date | 2003-01-30 | |
| dc.date.accessioned | 2026-07-07T04:54:46Z | |
| dc.date.available | 2026-07-07T04:54:46Z | |
| dc.description | We study cubical sets without degeneracies, which we call square sets. These sets arise naturally in a number of settings and they have a beautiful intrinsic geometry; in particular a square set C has an infinite family of associated square sets J^i(C), i=1,2,..., which we call James complexes. There are mock bundle projections p_i:|J^i(C)|-->|C| (which we call James bundles) defining classes in unstable cohomotopy which generalise the classical James--Hopf invariants of Omega(S^2). The algebra of these classes mimics the algebra of the cohomotopy of Omega(S^2) and the reduction to cohomology defines a sequence of natural characteristic classes for a square set. An associated map to BO leads to a generalised cohomology theory with geometric interpretation similar to that for Mahowald orientation [M Mahowald, Ring Spectra which are Thom complexes, Duke Math. J. 46 (1979) 549--559] and [B Sanderson, The geometry of Mahowald orientations, SLN 763 (1978) 152--174]. | |
| dc.description | This paper is extracted from our January 1996 preprint `James bundles and applications' available at: http://www.maths.warwick.ac.uk/~cpr/ftp/james.ps | |
| dc.identifier | https://arxiv.org/abs/math/0301354 | |
| dc.identifier | http://arxiv.org/abs/math/0301354 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66390 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 55N22, 55P44; 57R15, 57R20, 57R90 | |
| dc.title | James bundles | |
| dc.type | text |