Annali di Matematica Pura ed Applicata

, Volume 107, Issue 1, pp 131-157

Sui fibrati con struttura quaternionale generalizzata

  • Stefano MarchiafavaAffiliated with
  • , Giuliano RomaniAffiliated with

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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.