Bounding the gap between a free group (outer) automorphism and its inverse

Detalhes bibliográficos
Autor(a) principal: Pedro V. Silva
Data de Publicação: 2016
Outros Autores: Manuel Ladra, Enric Ventura
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/10216/110895
Resumo: For any finitely generated group G, two complexity functions alpha(G) and beta(G) are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of G and the norm of its inverse. Restricting attention to free groups F-r, the exact asymptotic behaviour of alpha(2) and beta(2) is computed. For rank r >= 3, polynomial lower bounds are provided for alpha(r) and beta(r), and the existence of a polynomial upper bound is proved for beta(r).
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spelling Bounding the gap between a free group (outer) automorphism and its inverseFor any finitely generated group G, two complexity functions alpha(G) and beta(G) are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of G and the norm of its inverse. Restricting attention to free groups F-r, the exact asymptotic behaviour of alpha(2) and beta(2) is computed. For rank r >= 3, polynomial lower bounds are provided for alpha(r) and beta(r), and the existence of a polynomial upper bound is proved for beta(r).20162016-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/110895eng0010-075710.1007/s13348-015-0133-3Pedro V. SilvaManuel LadraEnric Venturainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T15:08:18Zoai:repositorio-aberto.up.pt:10216/110895Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:16:31.298299Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Bounding the gap between a free group (outer) automorphism and its inverse
title Bounding the gap between a free group (outer) automorphism and its inverse
spellingShingle Bounding the gap between a free group (outer) automorphism and its inverse
Pedro V. Silva
title_short Bounding the gap between a free group (outer) automorphism and its inverse
title_full Bounding the gap between a free group (outer) automorphism and its inverse
title_fullStr Bounding the gap between a free group (outer) automorphism and its inverse
title_full_unstemmed Bounding the gap between a free group (outer) automorphism and its inverse
title_sort Bounding the gap between a free group (outer) automorphism and its inverse
author Pedro V. Silva
author_facet Pedro V. Silva
Manuel Ladra
Enric Ventura
author_role author
author2 Manuel Ladra
Enric Ventura
author2_role author
author
dc.contributor.author.fl_str_mv Pedro V. Silva
Manuel Ladra
Enric Ventura
description For any finitely generated group G, two complexity functions alpha(G) and beta(G) are defined to measure the maximal possible gap between the norm of an automorphism (respectively, outer automorphism) of G and the norm of its inverse. Restricting attention to free groups F-r, the exact asymptotic behaviour of alpha(2) and beta(2) is computed. For rank r >= 3, polynomial lower bounds are provided for alpha(r) and beta(r), and the existence of a polynomial upper bound is proved for beta(r).
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/10216/110895
url https://hdl.handle.net/10216/110895
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0010-0757
10.1007/s13348-015-0133-3
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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