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...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2008 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:21991 |
| Online Access: | https://ddd.uab.cat/record/21991 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_52108_03 |
| Access Level: | Open access |
| Keyword: | Thompson's groups Braid groups Pure braids Braided tree diagrams |
| Summary: | 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. |
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