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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

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

We exhibit a six dimensional manifold with a line bundle on it which is not the pullback of a bundle on S 2 .

Line bundles with c 1 L 2 = 0 . Higher order obstruction

Stefano De Michelis (1991)

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

We study secondary obstructions to representing a line bundle as the pull-back of a line bundle on S 2 and we interpret them geometrically.

Linear direct connections

Jan Kubarski, Nicolae Teleman (2007)

Banach Center Publications

In this paper we study the geometry of direct connections in smooth vector bundles (see N. Teleman [Tn.3]); we show that the infinitesimal part, τ , of a direct connection τ is a linear connection. We determine the curvature tensor of the associated linear connection τ . As an application of these results, we present a direct proof of N. Teleman’s Theorem 6.2 [Tn.3], which shows that it is possible to represent the Chern character of smooth vector bundles as the periodic cyclic homology class of a...

Linear hamiltonian circle actions that generate minimal Hilbert bases

Ágúst Sverrir Egilsson (2000)

Annales de l'institut Fourier

The orbit space of a linear Hamiltonian circle action and the reduced orbit space, at zero, are examples of singular Poisson spaces. The orbit space inherits the Poisson algebra of functions invariant under the linear circle action and the reduced orbit space inherits the Poisson algebra obtained by restricting the invariant functions to the reduced space. Both spaces reside inside smooth manifolds, which in turn inherit almost Poisson structures from the Poisson varieties. In this paper we consider...

Link bordism skein modules

Uwe Kaiser (2004)

Fundamenta Mathematicae

We compute link bordism skein modules of colored oriented links in oriented 3-manifolds. A Hurewicz theorem relating link bordism and link homotopy skein modules is proved.

Link cobordism.

Sylvain E. Cappell, Julius L. Shaneson (1980)

Commentarii mathematici Helvetici

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