Displaying similar documents to “ K -theory of oriented Grassmann manifolds”

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. ...

Contact topology and the structure of 5-manifolds with π 1 = ℤ 2

Hansjörg Geiges, Charles B. Thomas (1998)

Annales de l'institut Fourier

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We prove a structure theorem for closed, orientable 5-manifolds M with fundamental group π 1 ( M ) = ℤ 2 and second Stiefel-Whitney class equal to zero on H 2 ( M ) . This structure theorem is then used to construct contact structures on such manifolds by applying contact surgery to fake projective spaces and certain ℤ 2 -quotients of  S 2 × S 3 .