2018/04/17 by Russell Ricks, Ricks, Russell
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.1804.06374
Let X be a proper CAT(0) space and G a cocompact group of isometries of X without fixed point at infinity. We prove that if ∂ X contains an invariant subset of circumradius π/2, then X contains a quasi-dense, closed convex subspace that splits as a product. Adding the assumption that the G-action on X is properly discontinuous, we give more conditions that are equivalent to a product splitting. In particular, this occurs if ∂ X contains a proper nonempty, closed, invariant, π-convex set in ∂ X; or if some nonempty closed, invariant set in ∂ X intersects each round sphere K ⊂ ∂ X inside a proper subsphere of K.