Vector fields on non-compact manifolds
Geometric Topology
2024-12-18 v3 Algebraic Topology
Differential Geometry
Abstract
Let be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group . We establish a Poincar\'{e}-Hopf theorem for a bounded vector field on satisfying a mild condition on zeros. As an application, we show that such a vector field must have infinitely many zeros whenever is amenable and the Euler characteristic of is non-zero.
Cite
@article{arxiv.2211.00512,
title = {Vector fields on non-compact manifolds},
author = {Tsuyoshi Kato and Daisuke Kishimoto and Mitsunobu Tsutaya},
journal= {arXiv preprint arXiv:2211.00512},
year = {2024}
}
Comments
10 pages