Large Scale Geometry of 4-dimensional Closed Nonpositively Curved Real Analytic Manifolds

Details Large Scale Geometry of 4-dimensional Closed Nonpositively Curved Real Analytic Manifolds Large Scale Geometry of 4-dimensional Closed Nonpositively Curved Real Analytic Manifolds

2004-12-13

arxiv.org/abs/math/0412258v2

International Mathematics Research Notices 2005, no. 30, 1803--1815

Mathematics

Metric Geometry

13 pages; Minor changes. To appear in International Mathematics Research Notices (IMRN)

Scientific paper

We study the asymptotic cones of the universal covering spaces of closed
4-dimensional nonpositively curved real analytic manifolds. We show that the
existence of nonstandard components in the Tits boundary, discovered by
Christoph Hummel and Victor Schroeder, depends only on the quasi-isometry type
of the fundamental group.

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