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.
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 par difféomorphismes isotopiques à l’identité et n’admettant pas de prolongement à une action sur une variété de dimension 3 avec bord . Cela répond à une question posée dans les travaux antérieurs des auteurs.
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Accepted:
Published online:
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
@article{AIF_2022__72_3_989_0, author = {Mann, Kathryn and Nariman, Sam}, title = {On the bordism group for group actions on the torus}, journal = {Annales de l'Institut Fourier}, pages = {989--1009}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {72}, number = {3}, year = {2022}, doi = {10.5802/aif.3480}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3480/} }
TY - JOUR AU - Mann, Kathryn AU - Nariman, Sam TI - On the bordism group for group actions on the torus JO - Annales de l'Institut Fourier PY - 2022 SP - 989 EP - 1009 VL - 72 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3480/ DO - 10.5802/aif.3480 LA - en ID - AIF_2022__72_3_989_0 ER -
%0 Journal Article %A Mann, Kathryn %A Nariman, Sam %T On the bordism group for group actions on the torus %J Annales de l'Institut Fourier %D 2022 %P 989-1009 %V 72 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3480/ %R 10.5802/aif.3480 %G en %F AIF_2022__72_3_989_0
Mann, Kathryn; Nariman, Sam. On the bordism group for group actions on the torus. Annales de l'Institut Fourier, Volume 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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