Top degree $\ell^p$-homology and conformal dimension of buildings
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929652280328192 |
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| author | Neumann, Antonio López |
| author_facet | Neumann, Antonio López |
| contents | For a non-compact finite thickness building whose Davis apartment is an orientable pseudomanifold, we compute the supremum of the set of $p>1$ such that its top dimensional reduced $\ell^p$-cohomology is nonzero. We adapt the non-vanishing assertion of this result to any finite thickness building using the Bestvina realization. Using similar techniques, we generalize bounds obtained by Clais on the conformal dimension of some Gromov-hyperbolic buildings to any such building. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05808 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Top degree $\ell^p$-homology and conformal dimension of buildings Neumann, Antonio López Group Theory 20J06, 20F67, 22E41, 30L10, 43A15, 51E24 For a non-compact finite thickness building whose Davis apartment is an orientable pseudomanifold, we compute the supremum of the set of $p>1$ such that its top dimensional reduced $\ell^p$-cohomology is nonzero. We adapt the non-vanishing assertion of this result to any finite thickness building using the Bestvina realization. Using similar techniques, we generalize bounds obtained by Clais on the conformal dimension of some Gromov-hyperbolic buildings to any such building. |
| title | Top degree $\ell^p$-homology and conformal dimension of buildings |
| topic | Group Theory 20J06, 20F67, 22E41, 30L10, 43A15, 51E24 |
| url | https://arxiv.org/abs/2204.05808 |