Pure braid subgroups of braided Thompson's groups
Brady, Tom (Dublin City University. Department of Mathematics)
Burillo Puig, Josep (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV)
Cleary, Sean (The City College of New York & The CUNY Graduate Center. Department of Mathematics)
Stein, Melanie (Trinity College. Department of Mathematics)

Date:	2008
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Thompson's groups ; Braid groups ; Pure braids ; Braided tree diagrams
Published in:	Publicacions matemàtiques, V. 52 n. 1 (2008) p. 57-89, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/74464
DOI: 10.5565/PUBLMAT_52108_03

33 p, 302.2 KB

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