Annali di Matematica Pura ed Applicata

, Volume 107, Issue 1, pp 131–157

Sui fibrati con struttura quaternionale generalizzata

  • Stefano Marchiafava
  • Giuliano Romani
Article

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.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Stefano Marchiafava
    • 1
  • Giuliano Romani
    • 1
  1. 1.Roma

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