Growth tightness and genericity for word metrics from injective spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914214994509824 |
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| author | Ding, Lihuang Martínez-Granado, Dídac Zalloum, Abdul |
| author_facet | Ding, Lihuang Martínez-Granado, Dídac Zalloum, Abdul |
| contents | Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show that all finite generating sets resulting from taking large enough balls in the respective injective space yield word metrics where pseudo-Anosov maps are exponentially generic. We also show that growth tightness holds true for the Cayley graphs corresponding to these finite generating sets, providing a positive answer to a question by Arzhantseva, Cashen and Tao. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth tightness and genericity for word metrics from injective spaces Ding, Lihuang Martínez-Granado, Dídac Zalloum, Abdul Geometric Topology 57M60, 20F67 Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show that all finite generating sets resulting from taking large enough balls in the respective injective space yield word metrics where pseudo-Anosov maps are exponentially generic. We also show that growth tightness holds true for the Cayley graphs corresponding to these finite generating sets, providing a positive answer to a question by Arzhantseva, Cashen and Tao. |
| title | Growth tightness and genericity for word metrics from injective spaces |
| topic | Geometric Topology 57M60, 20F67 |
| url | https://arxiv.org/abs/2407.02378 |