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Connectedness
properties and splittings of groups with isolated flats
G Christopher Hruska and Kim Ruane |
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Algebraic & Geometric Topology 21 (2021) 755–800
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Abstract |
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We study groups and their splittings as graphs of groups. For one-ended groups with isolated flats we prove a theorem characterizing exactly when the visual boundary is locally connected. This characterization depends on whether the group has a certain type of splitting over a virtually abelian subgroup. In the locally connected case, we describe the boundary as a tree of metric spaces in the sense of Świątkowski. A significant tool used in the proofs of the above results is a general convex splitting theorem for arbitrary groups. If a group splits as a graph of groups with convex edge groups, then the vertex groups are also groups. |
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Keywords
nonpositive curvature, isolated flats, locally connected,
tree of metric compacta
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Mathematical Subject Classification 2010
Primary: 20E08, 20F67
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References |
Publication
Received: 4 August 2019
Revised: 17 December 2019
Accepted: 18 May 2020
Published: 25 April 2021
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Authors |
| G Christopher Hruska | |
| Department of Mathematical
Sciences University of Wisconsin-Milwaukee Milwaukee, WI United States |
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| Kim Ruane | |
| Department of Mathematics Tufts University Medford, MA United States |
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