Chern characters in equivariant basic cohomology

Wenran Liu

doi:10.5802/crmath.14

Differential geometry

Chern characters in equivariant basic cohomology

Wenran Liu ^1,²

¹ IMAG Université de Montpellier, Place Eugène Bataillon 34090 Montpellier, France
² SIAE Civil Aviation University of China, 2898 Jinbei Street Dongli District, 300300 Tianjin, China

Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 1-5.

Abstract
Résumé

The purpose of this Note is to establish a geometric realization of the cohomological isomorphism in the case of a transversely oriented Killing foliation on a compact smooth manifold through equivariant basic Chern characters.

L’objet de cette Note est d’établir une réalisation géométrique de l’isomorphisme cohomologique dans le cas d’un feuilletage de Killing transversalement orienté sur une variété compacte à travers les caractères de Chern basiques équivariants.

Received: 2019-09-09
Revised: 2019-10-18
Accepted: 2019-12-20
Published online: 2021-03-01

DOI: 10.5802/crmath.14

Author's affiliations:

Wenran Liu ^{1, 2}

¹ IMAG Université de Montpellier, Place Eugène Bataillon 34090 Montpellier, France
² SIAE Civil Aviation University of China, 2898 Jinbei Street Dongli District, 300300 Tianjin, China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Chern characters in equivariant basic cohomology},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1--5},
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     year = {2021},
     doi = {10.5802/crmath.14},
     language = {en},
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Wenran Liu. Chern characters in equivariant basic cohomology. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 1-5. doi : 10.5802/crmath.14. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.14/

References
Cited by

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[4] Oliver Goertsches; Dirk Toeben Equivariant basic cohomology of Riemannian foliations (2010) (https://arxiv.org/abs/1004.1043v1) | Zbl

[5] Alexander Gorokhovsky; John Lott The index of a transverse Dirac-type operator: the case of abelian Molino sheaf, J. Reine Angew. Math., Volume 678 (2013), pp. 125-162 | MR | Zbl

[6] Franz W. Kamber; Philippe Tondeur Foliated bundles and characteristic classes, Lecture Notes in Mathematics, 493, Springer, 1975 | Numdam | MR | Zbl

[7] Wenran Liu Chern characters in equivariant basic cohomology, Ph. D. Thesis, Université de Montpellier (France) (2017) (https://arxiv.org/abs/1803.03342)

[8] Pierre Molino Riemannian foliations, Progress in Mathematics, 73, Birkhäuser, 1988 | MR | Zbl

[9] Paul-Émile Paradan; Michèle Vergne Index of transversally elliptic operators, From probability to geometry II (Astérisque), Volume 328, Société Mathématique de France, 2009, pp. 297-338 | Numdam | Zbl

[10] Jean-Louis Tu La conjecture de Baum-Connes pour les feuilletages hyperboliques, Ph. D. Thesis, Université Paris 7 (France) (1996) (http://www.theses.fr/1996PA077291) | Zbl

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