Half dimensional collapse of ends of manifolds of nonpositive curvature

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Sep 14, 2016 - group, which we will call AΣ, which is generated by the abelian groups at all the other ... 9, that serves as a “center at infinity” of Ax in the sense.
arXiv:1608.02185v1 [math.GT] 7 Aug 2016

HALF DIMENSIONAL COLLAPSE OF ENDS OF MANIFOLDS OF NONPOSITIVE CURVATURE ˜ ˆ NGUYEN-PHAN ˆ GRIGORI AVRAMIDI, T. TAM Abstract. We study the topology of ends of noncompact, complete Riemannian n-manifolds M with bounded nonpositive sectional curvature and finite volume. It is known that if such a manifold is negatively curved or does not contain arbitrarily small geodesic loops, then it is tame in the sense that it is homeomorphic to the interior of a compact manifold M with boundary ∂M since the thin part M