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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...

Link cobordism.

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

Commentarii mathematici Helvetici

Linking and the Morse complex

Michael Usher (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

For a Morse function f on a compact oriented manifold M , we show that f has more critical points than the number required by the Morse inequalities if and only if there exists a certain class of link in M whose components have nontrivial linking number, such that the minimal value of f on one of the components is larger than its maximal value on the other. Indeed we characterize the precise number of critical points of f in terms of the Betti numbers of M and the behavior of f with respect to links....

Local density of diffeomorphisms with large centralizers

Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)

Annales scientifiques de l'École Normale Supérieure

Given any compact manifold M , we construct a non-empty open subset 𝒪 of the space Diff 1 ( M ) of C 1 -diffeomorphisms and a dense subset 𝒟 𝒪 such that the centralizer of every diffeomorphism in 𝒟 is uncountable, hence non-trivial.

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