Fenn, Roger, 1942-, Rourke, C. P. (Colin Patrick), 1943- and Sanderson, B. J. (Brian Joseph), 1939-. (2004) James bundles. Proceedings of the London Mathematical Society, Vol.89 (No.1). pp. 217-240. ISSN 0024-6115

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Abstract

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 Ji(C), for i = 1, 2, ..., which we call James complexes. There are mock bundle projections pi: |Ji(C)| -> |C| (which we call James bundles) defining classes in unstable cohomotopy which generalise the classical James–Hopf invariants of {Omega}(S2). The algebra of these classes mimics the algebra of the cohomotopy of {Omega}(S2) 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Algebraic topology, Manifolds (Mathematics), Differentiable manifolds, Cobordism theory, Differential topology
Journal or Publication Title:	Proceedings of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6115
Date:	July 2004
Volume:	Vol.89
Number:	No.1
Page Range:	pp. 217-240
Identification Number:	10.1112/S0024611504014674
Status:	Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/751

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