, Volume 107, Issue 1, pp 131-157

Sui fibrati con struttura quaternionale generalizzata

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Summary

Quaternion generalized fiber bundles \(\tilde E_n^\mathbb{Q} \to X\) are studied, both isomorphic to global tensorial product \(E_n^\mathbb{Q} \otimes _\mathbb{Q} E_1^\mathbb{Q} (E_n^\mathbb{Q} , E_1^\mathbb{Q}\) ordinary quaternion fiber bundles right and left respectively) and quite general ones. A cohomology class \(\varepsilon (\tilde E_n^\mathbb{Q} ) \in H^2 (X;\mathbb{Z}_2 )\) is considered which represents the obstruction in order the fiber bundle be a tensorial product. Several properties and a splitting principle are proved for bundles \(\tilde E_n^\mathbb{Q}\) . On this ground and founding on a convenient bundle BE → X associated to jaz (that we call Bonan's bundle and for which ɛ( \(\tilde E_n^\mathbb{Q}\) =ɛ(BE)) relations are stated among Stiefel-Whitney classes of \(\tilde E_n^\mathbb{Q}\) , BE and the class ɛ.

Entrata in Redazione il 14 agosto 1974.
Lavoro eseguito con contributo del C.N.R., nell'ambito del Gruppo Nazionale per le Strutture Algebriche e Geometriche e loro Applicazioni.