On limits of betweenness relations
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David Bradley-Williams
and
John K. Truss
Abstract
We give a flexible method for constructing a wide variety of limits of betweenness relations. This unifies work of Adeleke, who constructed a Jordan group preserving a limit of betweenness relations, and Bhattacharjee and Macpherson who gave an alternative method using a Fraïssé-type construction. A key ingredient in their work is the notion of a tree of 𝐵-sets. We employ this and extend its use to a wider class of examples.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: GRK 2240
Funding statement: This paper is based on part of the first author’s PhD thesis at the University of Leeds, 2014, which received DTG funding from the EPSRC. He is partially supported by the research training group GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and Topology, funded by the DFG.
Acknowledgements
D. Bradley-Williams would particularly like to thank Dugald Macpherson for introducing him to the topic of this paper, and for many helpful discussions during his time as a PhD student. The authors are grateful to the anonymous referee for suggestions that improved the presentation of this paper.
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Communicated by: John S. Wilson
References
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Articles in the same Issue
- Frontmatter
- Hochschild cohomology of symmetric groups and generating functions
- Stiefel–Whitney classes of representations of SL(2, 𝑞)
- A classification of finite primitive IBIS groups with alternating socle
- On the converse of Gaschütz’ complement theorem
- Conjugacy classes of maximal cyclic subgroups
- Morse boundaries of graphs of groups with finite edge groups
- The number of locally invariant orderings of a group
- On limits of betweenness relations
Articles in the same Issue
- Frontmatter
- Hochschild cohomology of symmetric groups and generating functions
- Stiefel–Whitney classes of representations of SL(2, 𝑞)
- A classification of finite primitive IBIS groups with alternating socle
- On the converse of Gaschütz’ complement theorem
- Conjugacy classes of maximal cyclic subgroups
- Morse boundaries of graphs of groups with finite edge groups
- The number of locally invariant orderings of a group
- On limits of betweenness relations
