Small cancellation and the Assouad-Nagata dimension of finitely generated groups
dc.contributor.advisor | Osin, Denis V | |
dc.creator | Sledd, Levi | |
dc.date.accessioned | 2022-02-02T21:35:10Z | |
dc.date.available | 2022-02-02T21:35:10Z | |
dc.date.created | 2022-01 | |
dc.date.issued | 2022-01-06 | |
dc.date.submitted | January 2022 | |
dc.identifier.uri | http://hdl.handle.net/1803/17045 | |
dc.description.abstract | We prove that the Assouad-Nagata dimension of any finitely generated (but not necessarily finitely presented) $C'(\sfrac{1}{6})$ group is at most 2. Using this result along with techniques of classical small cancellation theory, we construct, for every $k, m, n \in \mathbb N \cup \{\infty\}$ with $4 \leq k \leq m \leq n$, a finitely generated group with asymptotic dimension $k$ and Assouad-Nagata dimension $m$, which contains a finitely generated subgroup of Assouad-Nagata dimension $n$. This simultaneously answers two previously open questions in asymptotic dimension theory. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.subject | group theory | |
dc.subject | geometric group theory | |
dc.subject | small cancellation | |
dc.subject | asymptotic dimension | |
dc.subject | Assouad-Nagata dimension | |
dc.subject | van Kampen diagrams | |
dc.title | Small cancellation and the Assouad-Nagata dimension of finitely generated groups | |
dc.type | Thesis | |
dc.date.updated | 2022-02-02T21:35:10Z | |
dc.type.material | text | |
thesis.degree.name | PhD | |
thesis.degree.level | Doctoral | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University Graduate School | |
dc.creator.orcid | 0000-0002-0937-4071 | |
dc.contributor.committeeChair | Osin, Denis V |
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