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Fenn, Roger, Rourke, C. P. and Sanderson, B. J. (2004) James bundles. Proceedings of the London Mathematical Society, Vol.89 (No.1). pp. 217-240. doi:10.1112/S0024611504014674 ISSN 0024-6115.
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Official URL: http://dx.doi.org/10.1112/S0024611504014674
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Official Date: | July 2004 | ||||
Dates: |
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Volume: | Vol.89 | ||||
Number: | No.1 | ||||
Page Range: | pp. 217-240 | ||||
DOI: | 10.1112/S0024611504014674 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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