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On the relation between lifting obstructions and ordinary obstructions

โœ Scribed by Christian Bohr

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
95 KB
Volume
103
Category
Article
ISSN
0166-8641

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โœฆ Synopsis

We consider partial liftings k : A โ†’ E of maps f : X โ†’ B, where (X, A) is a relative CW-complex and E โ†’ B is a fibration. In this situation, we have a primary obstruction to extend the partial lifting to a lifting of f on all of X, and there is an obstruction to extend k as an ordinary map into the space E. A relation between these two cohomology classes is proved when the fibre of E โ†’ B is an Eilenberg-MacLane space K(ฮ , n) and ฯ€ i (E) = 0 for i q -1, where q n + 2, that specializes to well-known formulas about secondary obstructions. The result is applied to the Hopf fibration (what includes defect sections in S 1 -bundles over 4-manifolds) and to the case of a certain SU(3)-bundle over S 4 .

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