Secondary characteristic classes of super-foliations

Camille Laurent-Gengoux

doi:10.1016/j.crma.2004.06.006

Differential Geometry

Secondary characteristic classes of super-foliations
[Classes caractéristiques secondaires des super-feuilletages.]

Présenté par : Charles-Michel Marle

Camille Laurent-Gengoux ¹

¹ Department of Mathematics, Penn State University, University Park, PA 16802, USA

Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 567-572.

Résumé
Abstract

Nous déterminons des classes caractéristiques secondaires de super-feuilletages de codimension $0 + ε 1$ et $1 + ε 1$ . 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 $0 + ε 1$ and $1 + ε 1$ . 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 : 2004-02-09
Accepté le : 2004-06-05
Publié le : 2004-10-01

DOI : 10.1016/j.crma.2004.06.006

Affiliations des auteurs :

Camille Laurent-Gengoux ¹

¹ Department of Mathematics, Penn State University, University Park, PA 16802, USA

@article{CRMATH_2004__339_8_567_0,
     author = {Camille Laurent-Gengoux},
     title = {Secondary characteristic classes of super-foliations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {567--572},
     publisher = {Elsevier},
     volume = {339},
     number = {8},
     year = {2004},
     doi = {10.1016/j.crma.2004.06.006},
     language = {en},
}

TY  - JOUR
AU  - Camille Laurent-Gengoux
TI  - Secondary characteristic classes of super-foliations
JO  - Comptes Rendus. Mathématique
PY  - 2004
SP  - 567
EP  - 572
VL  - 339
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2004.06.006
LA  - en
ID  - CRMATH_2004__339_8_567_0
ER  -

%0 Journal Article
%A Camille Laurent-Gengoux
%T Secondary characteristic classes of super-foliations
%J Comptes Rendus. Mathématique
%D 2004
%P 567-572
%V 339
%N 8
%I Elsevier
%R 10.1016/j.crma.2004.06.006
%G en
%F CRMATH_2004__339_8_567_0

Camille Laurent-Gengoux. Secondary characteristic classes of super-foliations. Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 567-572. doi : 10.1016/j.crma.2004.06.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.006/

Bibliographie
Cité par

[1] D. Astashkevich; D.B. Fuchs 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] I.N. Bernshtein; B.I. Rozenfel'd 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] D.B. Fuks Characteristic classes of foliations, Russian Math. Surveys, Volume 28 (1973) no. 2, pp. 139-153

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

[8] J. Monterde; J. Mun̂oz-Masqué; O.A. Sánchez-Valenzuela 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

Cité par Sources :

Commentaires - Politique