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Journal Article
ON Sp(2) AND Sp(2) · Sp(1)-STRUCTURES IN 8-DIMENSIONAL VECTOR BUNDLES
Martin Čadek and Jiří Vanžura
Publicacions Matemàtiques
Vol. 41, No. 2 (1997), pp. 383-401
Published
by: Universitat Autònoma de Barcelona
https://www.jstor.org/stable/43737249
Page Count: 19
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Topics: Mathematical vectors, Mathematical manifolds, Tangents, Automorphisms, Subalgebras, Commutativity, Signatures, Sufficient conditions
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Abstract
Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(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 Sp(2)-structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.
Publicacions Matemàtiques
© 1997 Universitat Autònoma de Barcelona