Affine Maps Between CAT(0) Spaces

Abstract

We study affine maps between CAT(0) spaces with geometric actions, and show that they essentially split as products of dilations and linear maps (on the Euclidean factor). This extends known results from the Riemannian case. Furthermore, we prove a splitting lemma for the Tits boundary of a CAT(0) space with geometric action, a variant of a splitting lemma for geodesically complete CAT(1) spaces by Lytchak.

13 pages, 1 figure. V2: Filled gaps and corrected details of proofs in some arguments (particularly in Sections 3.1 and 3.2), other minor changes

References in corpus (2)

• A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
• Tits compact CAT(0) spaces