Detecting virtual homomorphisms via Banach metrics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908628507688960 |
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| author | Ron-George, Liran Yadin, Ariel |
| author_facet | Ron-George, Liran Yadin, Ariel |
| contents | We introduce the notion of "Banach metrics" on finitely generated infinite groups. This extends the notion of a Cayley graph (as a metric space). Our motivation comes from trying to detect the existence of virtual homomorphisms into Z, the additive group of integers. We show that detection of such homomorphisms through metric functional boundaries of Cayley graphs isn't always possible. However, we prove that it is always possible to do so through a metric functional boundary of some Banach metric on the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11543 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detecting virtual homomorphisms via Banach metrics Ron-George, Liran Yadin, Ariel Group Theory Metric Geometry 20F65, 51F30 We introduce the notion of "Banach metrics" on finitely generated infinite groups. This extends the notion of a Cayley graph (as a metric space). Our motivation comes from trying to detect the existence of virtual homomorphisms into Z, the additive group of integers. We show that detection of such homomorphisms through metric functional boundaries of Cayley graphs isn't always possible. However, we prove that it is always possible to do so through a metric functional boundary of some Banach metric on the group. |
| title | Detecting virtual homomorphisms via Banach metrics |
| topic | Group Theory Metric Geometry 20F65, 51F30 |
| url | https://arxiv.org/abs/2408.11543 |