Isodiametric and isoperimetric inequalities for complexes and groups
It is shown that D. Cohen's inequality bounding the isoperimetric function of a group by the double exponential of its isodiametric function is valid in the more general context of locally finite simply connected complexes. It is shown that in this context this bound is 'best possible'...
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| Format: | Journal article |
| Language: | English |
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2000
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| _version_ | 1797080337332830208 |
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| author | Papasoglu, P |
| author_facet | Papasoglu, P |
| author_sort | Papasoglu, P |
| collection | OXFORD |
| description | It is shown that D. Cohen's inequality bounding the isoperimetric function of a group by the double exponential of its isodiametric function is valid in the more general context of locally finite simply connected complexes. It is shown that in this context this bound is 'best possible'. Also studied are second-dimensional isoperimetric functions for groups and complexes. It is shown that the second-dimensional isoperimetric function of a group is bounded by a recursive function. By a similar argument it is shown that the area distortion of a finitely presented subgroup of a finitely presented group is recursive. Cohen's inequality is extended to second-dimensional isoperimetric and isodiametric functions of 2-connected simplicial complexes. |
| first_indexed | 2024-03-07T00:58:33Z |
| format | Journal article |
| id | oxford-uuid:88edf1c1-bcd8-455d-8674-f9b0ce5f577d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:58:33Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:88edf1c1-bcd8-455d-8674-f9b0ce5f577d2022-03-26T22:20:55ZIsodiametric and isoperimetric inequalities for complexes and groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:88edf1c1-bcd8-455d-8674-f9b0ce5f577dEnglishSymplectic Elements at Oxford2000Papasoglu, PIt is shown that D. Cohen's inequality bounding the isoperimetric function of a group by the double exponential of its isodiametric function is valid in the more general context of locally finite simply connected complexes. It is shown that in this context this bound is 'best possible'. Also studied are second-dimensional isoperimetric functions for groups and complexes. It is shown that the second-dimensional isoperimetric function of a group is bounded by a recursive function. By a similar argument it is shown that the area distortion of a finitely presented subgroup of a finitely presented group is recursive. Cohen's inequality is extended to second-dimensional isoperimetric and isodiametric functions of 2-connected simplicial complexes. |
| spellingShingle | Papasoglu, P Isodiametric and isoperimetric inequalities for complexes and groups |
| title | Isodiametric and isoperimetric inequalities for complexes and groups |
| title_full | Isodiametric and isoperimetric inequalities for complexes and groups |
| title_fullStr | Isodiametric and isoperimetric inequalities for complexes and groups |
| title_full_unstemmed | Isodiametric and isoperimetric inequalities for complexes and groups |
| title_short | Isodiametric and isoperimetric inequalities for complexes and groups |
| title_sort | isodiametric and isoperimetric inequalities for complexes and groups |
| work_keys_str_mv | AT papasoglup isodiametricandisoperimetricinequalitiesforcomplexesandgroups |