Vector fields on noncompact manifolds
Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3985-3996
Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
Let M be a noncompact connected manifold with a cocompact and properly discontinuous action of a discrete group G. We establish a Poincaré–Hopf theorem for a bounded vector field on M satisfying a mild condition on zeros. As an application, we show that such a vector field must have infinitely many zeros whenever G is amenable and the Euler characteristic of M∕G is nonzero.
Keywords:
vector field, noncompact manifold, bounded cohomology,
Poincaré–Hopf theorem
Affiliations des auteurs :
Kato, Tsuyoshi 1 ; Kishimoto, Daisuke 2 ; Tsutaya, Mitsunobu 2
@article{10_2140_agt_2024_24_3985,
author = {Kato, Tsuyoshi and Kishimoto, Daisuke and Tsutaya, Mitsunobu},
title = {Vector fields on noncompact manifolds},
journal = {Algebraic and Geometric Topology},
pages = {3985--3996},
publisher = {mathdoc},
volume = {24},
number = {7},
year = {2024},
doi = {10.2140/agt.2024.24.3985},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.3985/}
}
TY - JOUR AU - Kato, Tsuyoshi AU - Kishimoto, Daisuke AU - Tsutaya, Mitsunobu TI - Vector fields on noncompact manifolds JO - Algebraic and Geometric Topology PY - 2024 SP - 3985 EP - 3996 VL - 24 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.3985/ DO - 10.2140/agt.2024.24.3985 ID - 10_2140_agt_2024_24_3985 ER -
%0 Journal Article %A Kato, Tsuyoshi %A Kishimoto, Daisuke %A Tsutaya, Mitsunobu %T Vector fields on noncompact manifolds %J Algebraic and Geometric Topology %D 2024 %P 3985-3996 %V 24 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.3985/ %R 10.2140/agt.2024.24.3985 %F 10_2140_agt_2024_24_3985
Kato, Tsuyoshi; Kishimoto, Daisuke; Tsutaya, Mitsunobu. Vector fields on noncompact manifolds. Algebraic and Geometric Topology, Tome 24 (2024) no. 7, pp. 3985-3996. doi: 10.2140/agt.2024.24.3985
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