Leibniz cohomology for differentiable manifolds

Lodder, Jerry M.

doi:10.5802/aif.1611

Lodder, Jerry M.

Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 73-95.

Résumé
Abstract

On propose une définition de la cohomologie de Leibniz, $H L^{*}$ , pour les variétés différentiables. Alors $H L^{*}$ devient une version non-commutative de la cohomologie de Gelfand-Fuks. Les calculs de $H L^{*} (R^{n}; R)$ se réduisent à ceux des champs de vecteurs formels, et peuvent être identifiés avec des invariants de feuilletages.

We propose a definition of Leibniz cohomology, $H L^{*}$ , for differentiable manifolds. Then $H L^{*}$ becomes a non-commutative version of Gelfand-Fuks cohomology. The calculations of $H L^{*} (R^{n}; R)$ reduce to those of formal vector fields, and can be identified with certain invariants of foliations.

MR Zbl

DOI : 10.5802/aif.1611

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     title = {Leibniz cohomology for differentiable manifolds},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {1},
     year = {1998},
     doi = {10.5802/aif.1611},
     mrnumber = {99b:17003},
     zbl = {0912.17001},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1611/}
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Lodder, Jerry M. Leibniz cohomology for differentiable manifolds. Annales de l'Institut Fourier, Tome 48 (1998) no. 1, pp. 73-95. doi : 10.5802/aif.1611. http://archive.numdam.org/articles/10.5802/aif.1611/

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