Abstract
In this paper, we show some splitting theorems for CAT(0) spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non-positive curvature. A CAT(0) group Γ is said to be rigid, if Γ determines its boundary up to homeomorphisms of a CAT(0) space on which Γ acts geometrically. C. Croke and B. Kleiner have constructed a non-rigid CAT(0) group. As an application of the splitting theorems for CAT(0) spaces, we obtain that if Γ1 and Γ2 are rigid CAT(0) groups then so is Γ1 × Γ2.
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Partly supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan. (No. 21740037).
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Hosaka, T. On splitting theorems for CAT(0) spaces and compact geodesic spaces of non-positive curvature. Math. Z. 272, 1037–1050 (2012). https://doi.org/10.1007/s00209-011-0972-x
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DOI: https://doi.org/10.1007/s00209-011-0972-x