Geometriae Dedicata

, Volume 180, Issue 1, pp 1–16 | Cite as

Affine maps between CAT(0) spaces

Original Paper


We study affine maps between CAT(0) spaces with cocompact group 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 cocompact group action, a variant of a splitting lemma for geodesically complete CAT(1) spaces by Lytchak.


CAT(0) spaces Geometric actions Affine maps 



We thank Dan Guralnik and Eric Swenson for their inspiring paper [12], and Russell Ricks and Ben Schmidt for discussions of this paper. Ricks in particular suggested the simple proof of Lemma 3.7 and the reference for Theorem 2.3. We also thank the referee for a thorough report. The first two authors held postdoctoral fellowships at the University of Michigan, and are thankful for the excellent working environment provided.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Hanna Bennett
    • 1
  • Christopher Mooney
    • 2
  • Ralf Spatzier
    • 1
  1. 1.University of MichiganAnn ArborUSA
  2. 2.EpicVeronaUSA

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