Complete gradient shrinking Ricci solitons have finite topological type
  We show that a complete Riemannian manifold has finite topological type (i.e., homeomorphic to the interior of a compact manifold with boundary), provided its Bakry-\'{E}mery Ricci tensor has a positive lower bound, and either of the following conditions:   (i) the Ricci curvature is bounded from above; (ii) the Ricci curvature is bounded from below and injectivity radius is bounded away from zero.   Moreover, a complete shrinking Ricci soliton has finite topological type if its scalar curvature is bounded. 
Fuquan Fang, Jianwen man, Zhenlei Zhang