Pure braid subgroups of braided Thompson's groups

We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups BV and BVd which lead to natural presentations which emphasize one of their subgroup-containment prope...

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Detalles Bibliográficos
Autores: Brady, Tom, Burillo Puig, Josep, Cleary, Sean, Stein, Melanie
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:21991
Acceso en línea:https://ddd.uab.cat/record/21991
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_52108_03
Access Level:acceso abierto
Palabra clave:Thompson's groups
Braid groups
Pure braids
Braided tree diagrams
Descripción
Sumario:We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups BV and BVd which lead to natural presentations which emphasize one of their subgroup-containment properties. We consider pure braided versions of Thompson's group F. These groups, BF and BFd, are subgroups of the braided versions of Thompson's group V . Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus again preserving order. We define these pure braided groups, give normal forms for elements, and construct infinite and finite presentations of these groups.