Common overlattices in trees and trees with fins
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910023591919616 |
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| author | Shepherd, Sam |
| author_facet | Shepherd, Sam |
| contents | Bass and Kulkarni proved that any pair of free uniform lattices in the automorphism group of a tree have conjugates that both lie inside a third uniform lattice (which is not necessarily free). We show that this does not generalise to trees with fins. The construction of our counter-example involves working with a certain generalisation of the universal groups of Burger and Mozes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Common overlattices in trees and trees with fins Shepherd, Sam Group Theory 20F65 (Primary) 20E08, 22D05 (Secondary) Bass and Kulkarni proved that any pair of free uniform lattices in the automorphism group of a tree have conjugates that both lie inside a third uniform lattice (which is not necessarily free). We show that this does not generalise to trees with fins. The construction of our counter-example involves working with a certain generalisation of the universal groups of Burger and Mozes. |
| title | Common overlattices in trees and trees with fins |
| topic | Group Theory 20F65 (Primary) 20E08, 22D05 (Secondary) |
| url | https://arxiv.org/abs/2602.14646 |