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Displaying similar documents to “On the existence of 2-fields in 8-dimensional vector bundles over 8-complexes”

On S(2) and S(2) · S(1) structures in 8-dimensional vector bundles.

Martin Cadek, Jirí Vanzura (1997)

Publicacions Matemàtiques

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Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to S(2) or S(2) · S(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an S(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes. ...

Line bundles with c 1 ⁢ L 2 = 0

Stefano De Michelis (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We prove that on a C ⁢ W -complex the obstruction for a line bundle L to be the fractional power of a suitable pullback of the Hopf bundle on a 2-dimensional sphere is the vanishing of the square of the first Chern class of L . On the other hand we show that if one looks at integral powers then further secondary obstructions exist.