Line bundles with $ c_{1} (L)^{2} = 0 $. Higher order obstruction

Stefano De Michelis

Displaying similar documents to “Line bundles with $c_{1} {(L)}^{2} = 0$ . Higher order obstruction”

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.

Line bundles with $c_{1} {(L)}^{2} = 0$ . A six dimensional example

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 $S^{2}$ .

On oriented vector bundles over CW-complexes of dimension 6 and 7

Martin Čadek, Jiří Vanžura (1992)

Commentationes Mathematicae Universitatis Carolinae

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Necessary and sufficient conditions for the existence of $n$ -dimensional oriented vector bundles ( $n = 3, 4, 5$ ) over CW-complexes of dimension $\leq 7$ with prescribed Stiefel-Whitney classes $w_{2} = 0$ , $w_{4}$ and Pontrjagin class $p_{1}$ 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.

On the classification of oriented vector bundles over 5-complexes

Martin Čadek, Jiří Vanžura (1993)

Czechoslovak Mathematical Journal

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