The classification of orientable vector bundles over CW-complexes of small dimension

DOI10.1017/S0308210500032467zbMath0505.55017MaRDI QIDQ4741994

Lyndon M. Woodward

Publication date: 1982

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

homotopy of BSOPostnikov tower for BSOSO(n)-bundles over n- dimensional complexesstable orientable bundle over CW-complexes of dimension less than 9

Mathematics Subject Classification ID

Sphere bundles and vector bundles in algebraic topology (55R25) Homology and homotopy of (Bmathrm{O}) and (Bmathrm{U}); Bott periodicity (55R45) Classification of fiber spaces or bundles in algebraic topology (55R15)

Related Items (10)

The real K-ring of some CW-complexes of small dimension ⋮ Topological classification of complex vector bundles over 8-dimensional \(\mathrm{spin}^c\) manifolds ⋮ Fold maps on small dimensional manifolds with prescribed singular set ⋮ Classification of ``real Bloch-bundles: topological quantum systems of type AI ⋮ Special metrics and triality ⋮ Obstruction theory on 8-manifolds ⋮ On the classification of oriented 3-plane bundles over a 6-complex ⋮ Obstruction theory on 7-manifolds ⋮ On the gauge orbit types for theories with classical compact gauge group ⋮ Unnamed Item

Cites Work

• Some consequences of a theorem of Bott
• Classification of oriented sphere bundles over a 4-complex
• On simply connected, 4-dimensional polyhedra
• Cohomologie modulo 2 des complexes d'Eilenberg-MacLane
• On the parallelizability of the spheres
• Groupes de Lie et Puissances Reduites de Steenrod

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