Complete gradient shrinking Ricci solitons have finite topological type

2007/12/31 by Fuquan Fang, Fang, Fuquan, Jian-wen Man +4 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.0801.0103

arxiv created 2007/12/31 · arxiv updated 2009/12/01

Abstract

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-Émery 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.

Cited by

• Topology at infinity of complete gradient Schouten solitons
• Convergence of compact Ricci solitons

Related

• Complete Shrinking Ricci Solitons have Finite Fundamental Group
• Gradient Shrinking Ricci Solitons and Modified Sectional Curvature
• On Locally Conformally Flat Gradient Shrinking Ricci Solitons
• Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons
• The volume growth of complete gradient shrinking Ricci solitons