Calculating the virtual cohomological dimension of the automorphism group of a RAAG
We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right‐angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis‐conjugating automorphism groups. The main new tool is t...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Wiley
2020
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| _version_ | 1826278083073671168 |
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| author | Day, MB Sale, AW Wade, RD |
| author_facet | Day, MB Sale, AW Wade, RD |
| author_sort | Day, MB |
| collection | OXFORD |
| description | We describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right‐angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis‐conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe–Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups.
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| first_indexed | 2024-03-06T23:38:38Z |
| format | Journal article |
| id | oxford-uuid:6e856083-6be6-42b0-a157-ab640edc8fb0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:38:38Z |
| publishDate | 2020 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:6e856083-6be6-42b0-a157-ab640edc8fb02022-03-26T19:25:05ZCalculating the virtual cohomological dimension of the automorphism group of a RAAGJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6e856083-6be6-42b0-a157-ab640edc8fb0EnglishSymplectic ElementsWiley2020Day, MBSale, AWWade, RDWe describe an algorithm to find the virtual cohomological dimension of the automorphism group of a right‐angled Artin group. The algorithm works in the relative setting; in particular, it also applies to untwisted automorphism groups and basis‐conjugating automorphism groups. The main new tool is the construction of free abelian subgroups of certain Fouxe–Rabinovitch groups of rank equal to their virtual cohomological dimension, generalizing a result of Meucci in the setting of free groups. |
| spellingShingle | Day, MB Sale, AW Wade, RD Calculating the virtual cohomological dimension of the automorphism group of a RAAG |
| title | Calculating the virtual cohomological dimension of the automorphism group of a RAAG |
| title_full | Calculating the virtual cohomological dimension of the automorphism group of a RAAG |
| title_fullStr | Calculating the virtual cohomological dimension of the automorphism group of a RAAG |
| title_full_unstemmed | Calculating the virtual cohomological dimension of the automorphism group of a RAAG |
| title_short | Calculating the virtual cohomological dimension of the automorphism group of a RAAG |
| title_sort | calculating the virtual cohomological dimension of the automorphism group of a raag |
| work_keys_str_mv | AT daymb calculatingthevirtualcohomologicaldimensionoftheautomorphismgroupofaraag AT saleaw calculatingthevirtualcohomologicaldimensionoftheautomorphismgroupofaraag AT waderd calculatingthevirtualcohomologicaldimensionoftheautomorphismgroupofaraag |