no. 3
On the bordism group for group actions on the torus
[Sur le groupe de bordisme pour l’action d’un groupe sur le tore]
Mann, Kathryn1 ; Nariman, Sam2
1 Department of Mathematics Cornell University Ithaca, NY, 14850 (USA)
2 Department of Mathematics Purdue University 150 N. University Street West Lafayette, IN 47907-2067 (USA)
Annales de l'Institut Fourier, Tome 72 (2022) no. 3, pp. 989-1009.

Dans cette courte note, nous étudions le groupe de bordisme pour l’action d’un groupe sur le tore et nous donnons quelques exemples de groupes agissant sur le tore T par difféomorphismes isotopiques à l’identité et n’admettant pas de prolongement à une action sur une variété de dimension 3 avec bord T. Cela répond à une question posée dans les travaux antérieurs des auteurs.

In this short note, we study the bordism problem for group actions on the torus and give examples of groups acting on the torus by diffeomorphisms isotopic to the identity that cannot be extended to an action on a bounding 3-manifold. This solves a question raised in the previous work of the authors.

Reçu le :
Révisé le :
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DOI : 10.5802/aif.3480
Classification : 57R50, 57R19, 57M60, 19J35, 55R40, 37C85
Keywords: Bordism, Diffeomorphism groups, Thompson’s group, Geometric 3-manifolds, Euler class
Mot clés : Bordisme, groupes de difféomorphisme, groupe de Thompson, variétés géometriques en dimension 3, classe d’Euler

Mann, Kathryn 1 ; Nariman, Sam 2

1 Department of Mathematics Cornell University Ithaca, NY, 14850 (USA)
2 Department of Mathematics Purdue University 150 N. University Street West Lafayette, IN 47907-2067 (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mann, Kathryn; Nariman, Sam. On the bordism group for group actions on the torus. Annales de l'Institut Fourier, Tome 72 (2022) no. 3, pp. 989-1009. doi : 10.5802/aif.3480. https://aif.centre-mersenne.org/articles/10.5802/aif.3480/

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