Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912589613629440 |
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| author | Grayevsky, Ido Pallier, Gabriel |
| author_facet | Grayevsky, Ido Pallier, Gabriel |
| contents | We establish distortion estimates in completely solvable Lie groups, using a sublinear bilipschitz retraction constructed by Cornulier, and interpolating between two theorems of Osin. This provides new lower bounds on Dehn functions. Our second main result is the quasiisometric rigidity of $\rm{Sol}_5$ and its lattices. Together with a theorem of Peng, a key tool for the rigidity is the complete list of Dehn functions and dimensions of asymptotic cones of all simply connected solvable Lie groups of exponential growth up to dimension $5$, which we compute using Cornulier and Tessera's results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12823 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$ Grayevsky, Ido Pallier, Gabriel Group Theory Metric Geometry 20F65 We establish distortion estimates in completely solvable Lie groups, using a sublinear bilipschitz retraction constructed by Cornulier, and interpolating between two theorems of Osin. This provides new lower bounds on Dehn functions. Our second main result is the quasiisometric rigidity of $\rm{Sol}_5$ and its lattices. Together with a theorem of Peng, a key tool for the rigidity is the complete list of Dehn functions and dimensions of asymptotic cones of all simply connected solvable Lie groups of exponential growth up to dimension $5$, which we compute using Cornulier and Tessera's results. |
| title | Dehn functions: computations, lower bounds, and the quasiisometric rigidity of $\rm{Sol}_5$ |
| topic | Group Theory Metric Geometry 20F65 |
| url | https://arxiv.org/abs/2509.12823 |