Affine Maps Between CAT(0) Spaces
Geometric Topology
2014-10-09 v2
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.
Cite
@article{arxiv.1309.1013,
title = {Affine Maps Between CAT(0) Spaces},
author = {Hanna Bennett and Christopher Mooney and Ralf Spatzier},
journal= {arXiv preprint arXiv:1309.1013},
year = {2014}
}
Comments
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