Property (QT) of relatively hierarchically hyperbolic groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910191125004288 |
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| author | Tao, Bingxue |
| author_facet | Tao, Bingxue |
| contents | Using the projection complex machinery, Bestvina-Bromberg-Fujiwara, Hagen-Petyt and Han-Nguyen-Yang prove that several classes of nonpositively-curved groups admit equivariant quasi-isometric embeddings into finite products of quasi-trees, i.e. having property (QT). In this paper, we unify and generalize the above results by establishing a sufficient condition for relatively hierarchically hyperbolic groups to have property (QT).
As applications, we show that a group has property (QT) if it is residually finite and belongs to one of the following classes of groups: admissible groups, hyperbolic--$2$--decomposable groups with no distorted elements, Artin groups of large and hyperbolic type. We also introduce a slightly stronger version of property (QT), called property (QT'), and show the invariance of property (QT') under graph products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20065 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Property (QT) of relatively hierarchically hyperbolic groups Tao, Bingxue Group Theory Geometric Topology Using the projection complex machinery, Bestvina-Bromberg-Fujiwara, Hagen-Petyt and Han-Nguyen-Yang prove that several classes of nonpositively-curved groups admit equivariant quasi-isometric embeddings into finite products of quasi-trees, i.e. having property (QT). In this paper, we unify and generalize the above results by establishing a sufficient condition for relatively hierarchically hyperbolic groups to have property (QT). As applications, we show that a group has property (QT) if it is residually finite and belongs to one of the following classes of groups: admissible groups, hyperbolic--$2$--decomposable groups with no distorted elements, Artin groups of large and hyperbolic type. We also introduce a slightly stronger version of property (QT), called property (QT'), and show the invariance of property (QT') under graph products. |
| title | Property (QT) of relatively hierarchically hyperbolic groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2412.20065 |