The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces
We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fn) has a fied point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826306781293314048 |
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| author | Bridson, M |
| author_facet | Bridson, M |
| author_sort | Bridson, M |
| collection | OXFORD |
| description | We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fn) has a fied point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated Z4 ⊂ Aut(F3) leaves invariant an isometrically embedded copy of Euclidean 3-space E3 → X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet domain. An abundance of actions of the second kind is described. Constraints on maps from Aut(Fn) to mapping class groups and linear groups are obtained. If n ≥ 2 then neither Aut(Fn) nor Out(F n) is the fundamental group of a compact Kähler manifold. © Instytut Matematyczny PAN, 2011. |
| first_indexed | 2024-03-07T06:53:07Z |
| format | Journal article |
| id | oxford-uuid:fd338519-f0ab-4fa0-902d-457f195d7fa4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:53:07Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:fd338519-f0ab-4fa0-902d-457f195d7fa42022-03-27T13:27:05ZThe rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fd338519-f0ab-4fa0-902d-457f195d7fa4EnglishSymplectic Elements at Oxford2011Bridson, MWe consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fn) has a fied point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated Z4 ⊂ Aut(F3) leaves invariant an isometrically embedded copy of Euclidean 3-space E3 → X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet domain. An abundance of actions of the second kind is described. Constraints on maps from Aut(Fn) to mapping class groups and linear groups are obtained. If n ≥ 2 then neither Aut(Fn) nor Out(F n) is the fundamental group of a compact Kähler manifold. © Instytut Matematyczny PAN, 2011. |
| spellingShingle | Bridson, M The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces |
| title | The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces |
| title_full | The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces |
| title_fullStr | The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces |
| title_full_unstemmed | The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces |
| title_short | The rhombic dodecahedron and semisimple actions of Aut(F-n) on CAT (0) spaces |
| title_sort | rhombic dodecahedron and semisimple actions of aut f n on cat 0 spaces |
| work_keys_str_mv | AT bridsonm therhombicdodecahedronandsemisimpleactionsofautfnoncat0spaces AT bridsonm rhombicdodecahedronandsemisimpleactionsofautfnoncat0spaces |