no. 8
Differential Geometry
Secondary characteristic classes of super-foliations
[Classes caractéristiques secondaires des super-feuilletages.]

Présenté par : Charles-Michel Marle

Laurent-Gengoux, Camille1
1 Department of Mathematics, Penn State University, University Park, PA 16802, USA
Comptes Rendus. Mathématique, Tome 339 (2004) no. 8, pp. 567-572.

Nous déterminons des classes caractéristiques secondaires de super-feuilletages de codimension 0+ε1 et 1+ε1. Nous indiquons comment généraliser cette construction pour les feuilletages réguliers de codimension quelconque sur des super-variétés. Nous interprètons ensuite les classes ainsi construites comme des classes caractéristiques associées à des connexions feuilletées plates.

We construct secondary classes for super-foliations of codimension 0+ε1 and 1+ε1. We indicate how to generalize this construction for any regular super-foliations on super-manifolds. We interpret the secondary classes as classes of foliated flat connections.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.06.006
Laurent-Gengoux, Camille 1

1 Department of Mathematics, Penn State University, University Park, PA 16802, USA 
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Laurent-Gengoux, Camille. Secondary characteristic classes of super-foliations. Comptes Rendus. Mathématique, Tome 339 (2004) no. 8, pp. 567-572. doi : 10.1016/j.crma.2004.06.006. http://www.numdam.org/articles/10.1016/j.crma.2004.06.006/

[1] Astashkevich, D.; Fuchs, D.B. On the cohomology of the Lie super-algebra W(m|n). Unconventional Lie algebras, Adv. Soviet Math., vol. 17, American Mathematical Society, Providence, RI, 1993, pp. 1-13

[2] Bernshtein, I.N.; Rozenfel'd, B.I. Homogeneous spaces of infinite dimensional Lie algebras and characteristic classes of foliations, Uspekhi Mat. Nauk, Volume 28 (1973) no. 4(172), pp. 103-138

[3] Fuks, D.B. Characteristic classes of foliations, Russian Math. Surveys, Volume 28 (1973) no. 2, pp. 139-153

[4] Fuks, D.B. Cohomology of Infinite-Dimensional Lie Algebras, Contemp. Soviet Math., vol. XII, Consultants Bureau, New York, 1986 (Translated from the Russian by A.B. Sosinskij)

[5] Koszul, J.-L. Les superalgèbres de Lie W(n) et leurs représentations. Géométrie différentielle, Travaux en Cours, vol. 33, Hermann, 1988, pp. 161-171

[6] C. Laurent-Gengoux, Characteristic classes of super-foliations, Preprint

[7] Leı̆tes, D.A. Introduction to the theory of super-manifolds, Uspekhi Mat. Nauk, Volume 35 (1980) no. 1(211), pp. 3-57 (in Russian)

[8] Monterde, J.; Mun̂oz-Masqué, J.; Sánchez-Valenzuela, O.A. Geometric properties of involutive distributions on graded manifolds, Indag. Mat. (N.S.), Volume 8 (1997), pp. 217-246

[9] G.M. Tuynman, Supermanifolds and Super Lie Groups: Basic Theory, Kluwer Academic, in press

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