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 study secondary obstructions to representing a line bundle as the pull-back of a line bundle on and we interpret them geometrically.
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 exhibit a six dimensional manifold with a line bundle on it which is not the pullback of a bundle on .
Martin Čadek, Jiří Vanžura (1992)
Commentationes Mathematicae Universitatis Carolinae
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Necessary and sufficient conditions for the existence of -dimensional oriented vector bundles () over CW-complexes of dimension with prescribed Stiefel-Whitney classes , and Pontrjagin class are found. As a consequence some results on the span of 6 and 7-dimensional oriented vector bundles are given in terms of characteristic classes.
J. Kurek, W. M. Mikulski (2004)
Annales Polonici Mathematici
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For natural numbers r,s,q,m,n with s ≥ r ≤ q we describe all natural affinors on the (r,s,q)-cotangent bundle over an (m,n)-dimensional fibered manifold Y.
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. ...
Stefan Wagner (2011)
Banach Center Publications
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A (smooth) dynamical system with transformation group ⁿ is a triple (A,ⁿ,α), consisting of a unital locally convex algebra A, the n-torus ⁿ and a group homomorphism α: ⁿ → Aut(A), which induces a (smooth) continuous action of ⁿ on A. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of trivial principal ⁿ-bundles based on such dynamical systems, i.e., we call a dynamical system (A,ⁿ,α) a trivial noncommutative principal ⁿ-bundle if each isotypic...