Cheeger-Gromoll Splitting Theorem for groups

Abstract

We study a notion of curvature for finitely generated groups which serves as a role of Ricci curvature for Riemannian manifolds. We prove an analog of Cheeger-Gromoll splitting theorem. As a consequence, we give a geometric characterization of virtually abelian groups. We also explore the relation between this notion of curvature and the growth of groups.

arXiv comment20 pages, 2 figures. Minor changes, final version to appear in Algebr. Geom. Topol