JournalsggdVol. 14, No. 1pp. 283–295

Boundary conditions detecting product splittings of CAT(0) spaces

  • Russell Ricks

    Binghamton University, USA
Boundary conditions detecting product splittings of CAT(0) spaces cover

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Abstract

Let XX be a proper CAT(0) space and GG a group of isometries of XX acting cocompactly without fixed point at infinity. We prove that if X\partial X contains an invariant subset of circumradius π/2\pi/2, then XX contains a quasi-dense, closed convex subspace that splits as a product.

Adding the assumption that the GG-action on XX is properly discontinuous, we give more conditions that are equivalent to a product splitting. In particular, this occurs if X\partial X contains a proper nonempty, closed, invariant, π\pi-convex set in X\partial X; or if some nonempty closed, invariant set in X\partial X intersects every round sphere KXK \subset \partial X inside a proper subsphere of KK.

Cite this article

Russell Ricks, Boundary conditions detecting product splittings of CAT(0) spaces. Groups Geom. Dyn. 14 (2020), no. 1, pp. 283–295

DOI 10.4171/GGD/544