Complete subamanifolds of ${\mathbb{R}}^n$ with finite topology

G. Pacelli Bessa, L. Jorge, J. Fabio Montenegro

We show that a complete $m$-dimensional immersed submanifold $M$ of ${\mathbb{R}}^n$ with $a(M)<1$ is properly immersed and have finite topology, where $a(M)\in [0,\infty ]$ is an s…