On the biautomaticity of CAT(0) triangle-square groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911193467191296 |
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| author | Kandybo, Mateusz |
| author_facet | Kandybo, Mateusz |
| contents | Following the research from the paper "Triangles, squares and geodesics" (arXiv:0910.5688) of Rena Levitt and Jon McCammond we investigate the properties of groups acting on CAT(0) triangle-square complexes, focusing mostly on biautomaticity of such groups. In particular we show two examples of nonpositively curved triangle-square complexes $X_1$ and $X_2$, such that their universal covers violate conjectures given in the aforementioned paper. This shows that the Gersten-Short geodesics cannot be used as a way of proving biautomaticity of groups acting on such complexes. Lastly we give a proof of biautomaticity of $π_1(X_1)$, however the biautomaticity of $π_1(X_2)$ remains unknown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the biautomaticity of CAT(0) triangle-square groups Kandybo, Mateusz Group Theory 20F67 (Primary) 20F65, 20F10 (Secondary) Following the research from the paper "Triangles, squares and geodesics" (arXiv:0910.5688) of Rena Levitt and Jon McCammond we investigate the properties of groups acting on CAT(0) triangle-square complexes, focusing mostly on biautomaticity of such groups. In particular we show two examples of nonpositively curved triangle-square complexes $X_1$ and $X_2$, such that their universal covers violate conjectures given in the aforementioned paper. This shows that the Gersten-Short geodesics cannot be used as a way of proving biautomaticity of groups acting on such complexes. Lastly we give a proof of biautomaticity of $π_1(X_1)$, however the biautomaticity of $π_1(X_2)$ remains unknown. |
| title | On the biautomaticity of CAT(0) triangle-square groups |
| topic | Group Theory 20F67 (Primary) 20F65, 20F10 (Secondary) |
| url | https://arxiv.org/abs/2412.02892 |