Localization of basic characteristic classes
Annales de l'Institut Fourier, Volume 64 (2014) no. 2, p. 537-570

We introduce basic characteristic classes and numbers as new invariants for Riemannian foliations. If the ambient Riemannian manifold M is complete, simply connected (or more generally if the foliation is a transversely orientable Killing foliation) and if the space of leaf closures is compact, then the basic characteristic numbers are determined by the infinitesimal dynamical behavior of the foliation at the union of its closed leaves. In fact, they can be computed with an Atiyah-Bott-Berline-Vergne-type localization theorem for equivariant basic cohomology.

Nous introduisons des classes et des nombres caractéristiques basiques d’un feuilletage riemannien. Si la variété riemannienne est complète, simplement connexe (ou plus généralement si le feuilletage est un feuilletage de Killing transversalement orientable) et si l’espace des ahérences des feuilles est compact, alors les nombres caractéristiques basiques sont déterminés par la dynamique infinitésimale du feuilletage en l’union des adhérences des feuilles fermées. En effet, ils peuvent être calculés avec un théorème de localisation de type Atiyah-Bott-Berline-Vergne pour la cohomologie équivariante basique.

DOI : https://doi.org/10.5802/aif.2857
Classification:  57R30,  53C12,  57R20
Keywords: Riemannian foliations, basic cohomology, equivariant cohomology, characteristic classes, localization
@article{AIF_2014__64_2_537_0,
     author = {T\"oben, Dirk},
     title = {Localization of basic characteristic classes},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {2},
     year = {2014},
     pages = {537-570},
     doi = {10.5802/aif.2857},
     mrnumber = {3330914},
     zbl = {06387284},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_2_537_0}
}
Localization of basic characteristic classes. Annales de l'Institut Fourier, Volume 64 (2014) no. 2, pp. 537-570. doi : 10.5802/aif.2857. http://www.numdam.org/item/AIF_2014__64_2_537_0/

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