论文标题
非压缩歧管上的向量场
Vector fields on non-compact manifolds
论文作者
论文摘要
令$ m $是一种非紧密连接的歧管，具有离散组$ g $的共同体和正确连续的动作。我们在$ m $上建立了一个有界矢量场的庞加尔 - 霍普定理，满足零件的温和条件。作为一个应用程序，我们表明，每当$ g $都可以正常使用，并且$ m/g $的欧拉特性是非零的。
Let $M$ be a non-compact 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 non-zero.
