Tits geometry associated with 4-dimensional closed real-analytic manifolds of nonpositive curvature

Abstract

We investigate the geometry and topology of the Tits boundary associated with 4-dimensional closed, real-analytic manifolds of nonpositive curvature. We show that each homotopically nontrivial component is a union of geometric boundaries of flats in the corresponding Hadamard manifold and this can be used to describe the structure of its maximal dimensional quasi-flats. The homotopically trivial components are intervals of length smaller than π and we give a necessary and sufficient criterion for the existence of such intervals of length grater than zero.