Expanders, rank and graphs of groups
Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or HNN extension, for infinitely many i; 2. the Cayley graphs of...
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1797100212412481536 |
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| author | Lackenby, M |
| author_facet | Lackenby, M |
| author_sort | Lackenby, M |
| collection | OXFORD |
| description | Let G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or HNN extension, for infinitely many i; 2. the Cayley graphs of G/G_i (with respect to a fixed finite set of generators for G) form an expanding family; 3. inf_i (d(G_i)-1)/[G:G_i] = 0, where d(G_i) is the rank of G_i. The proof involves an analysis of the geometry and topology of finite Cayley graphs. Several applications of this result are given. |
| first_indexed | 2024-03-07T05:34:31Z |
| format | Journal article |
| id | oxford-uuid:e36caeaf-e002-4326-a563-af5ca9e089ef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:34:31Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:e36caeaf-e002-4326-a563-af5ca9e089ef2022-03-27T10:09:06ZExpanders, rank and graphs of groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e36caeaf-e002-4326-a563-af5ca9e089efEnglishSymplectic Elements at Oxford2004Lackenby, MLet G be a finitely presented group, and let {G_i} be a collection of finite index normal subgroups that is closed under intersections. Then, we prove that at least one of the following must hold: 1. G_i is an amalgamated free product or HNN extension, for infinitely many i; 2. the Cayley graphs of G/G_i (with respect to a fixed finite set of generators for G) form an expanding family; 3. inf_i (d(G_i)-1)/[G:G_i] = 0, where d(G_i) is the rank of G_i. The proof involves an analysis of the geometry and topology of finite Cayley graphs. Several applications of this result are given. |
| spellingShingle | Lackenby, M Expanders, rank and graphs of groups |
| title | Expanders, rank and graphs of groups |
| title_full | Expanders, rank and graphs of groups |
| title_fullStr | Expanders, rank and graphs of groups |
| title_full_unstemmed | Expanders, rank and graphs of groups |
| title_short | Expanders, rank and graphs of groups |
| title_sort | expanders rank and graphs of groups |
| work_keys_str_mv | AT lackenbym expandersrankandgraphsofgroups |