Aut-invariant quasimorphisms on groups
For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended finitely generated groups, some relatively hyperbolic groups, and...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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American Mathematical Society
2023
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| _version_ | 1797110753693532160 |
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| author | Fournier-Facio, F Wade, RD |
| author_facet | Fournier-Facio, F Wade, RD |
| author_sort | Fournier-Facio, F |
| collection | OXFORD |
| description | For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended finitely generated groups, some relatively hyperbolic groups, and a class of graph products of groups that includes all right-angled Artin and Coxeter groups that are not virtually abelian.
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This was known for F2 by a result of Brandenbursky and Marcinkowski [Comment. Math. Helv. 94 (2019), pp. 661–687], but is new even for free groups of higher rank, settling a question of Miklós Abért. The case of graph products of finitely generated abelian groups settles a question of Michał Marcinkowski. As a consequence, we deduce that a variety of Aut-invariant norms on such groups are unbounded. |
| first_indexed | 2024-03-07T07:59:16Z |
| format | Journal article |
| id | oxford-uuid:9983644c-43ab-4a5a-8f4c-24d8b52e73ca |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:59:16Z |
| publishDate | 2023 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:9983644c-43ab-4a5a-8f4c-24d8b52e73ca2023-09-15T11:37:59ZAut-invariant quasimorphisms on groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9983644c-43ab-4a5a-8f4c-24d8b52e73caEnglishSymplectic ElementsAmerican Mathematical Society2023Fournier-Facio, FWade, RDFor a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended finitely generated groups, some relatively hyperbolic groups, and a class of graph products of groups that includes all right-angled Artin and Coxeter groups that are not virtually abelian. <br> This was known for F2 by a result of Brandenbursky and Marcinkowski [Comment. Math. Helv. 94 (2019), pp. 661–687], but is new even for free groups of higher rank, settling a question of Miklós Abért. The case of graph products of finitely generated abelian groups settles a question of Michał Marcinkowski. As a consequence, we deduce that a variety of Aut-invariant norms on such groups are unbounded. |
| spellingShingle | Fournier-Facio, F Wade, RD Aut-invariant quasimorphisms on groups |
| title | Aut-invariant quasimorphisms on groups |
| title_full | Aut-invariant quasimorphisms on groups |
| title_fullStr | Aut-invariant quasimorphisms on groups |
| title_full_unstemmed | Aut-invariant quasimorphisms on groups |
| title_short | Aut-invariant quasimorphisms on groups |
| title_sort | aut invariant quasimorphisms on groups |
| work_keys_str_mv | AT fournierfaciof autinvariantquasimorphismsongroups AT waderd autinvariantquasimorphismsongroups |