Half dimensional collapse of ends of manifolds of nonpositive curvature

Avramidi, Grigori; Nguyễn Phan, T. Tâm

doi:10.1007/s00039-019-00515-2

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Half dimensional collapse of ends of manifolds of nonpositive curvature

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Avramidi, Grigori
Max Planck Institute for Mathematics, Max Planck Society;

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Nguyễn Phan, T. Tâm
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Avramidi, G., & Nguyễn Phan, T. T. (2019). Half dimensional collapse of ends of manifolds of nonpositive curvature. Geometric and Functional Analysis, 29(6), 1638-1702. doi:10.1007/s00039-019-00515-2.

Cite as: https://hdl.handle.net/21.11116/0000-0005-5D47-4

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 $\lfloor n/2\rfloor$.