Half dimensional collapse of ends of manifolds of nonpositive curvature

Abstract

This paper accomplishes two things. First, we construct a geometric analog of the rational Tits building for general noncompact, complete, finite volume $n$-manifolds $M$ of bounded nonpositive curvature. Second, we prove that this analog has dimension less than $\lfloor n/2\rfloor$.

arXiv commentThis version is a remake that is significantly different from the older ones. The theorems are mostly the same though the content has been much altered and thus this makes almost a completely different paper. 68 pages, 14 figures