Affine Maps Between CAT(0) Spaces

2013/09/04 by Hanna Bennett, Bennett, Hanna, Christopher Park Mooney +4
Mathematics · #20F67 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:20F67

paper · pdf · doi:10.48550/arxiv.1309.1013

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

openalex publication_date 2013/09/04 · arxiv created 2014/10/07 · arxiv updated 2014/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry

Related

• On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature
• Thin actions on CAT(0) spaces
• Natural maps between CAT(0) boundaries
• Tits compact CAT(0) spaces
• On equivariant homeomorphisms of boundaries of CAT(0) groups