Quasi-positivity and recognition of products of conjugacy classes in free groups
| Autor: | Bell, Robert W., Gitik, Rita |
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| Rok vydání: | 2018 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Given a group $G$ and a subset $X \subset G$, an element $g \in G$ is called quasi-positive if it is equal to a product of conjugates of elements in the semigroup generated by $X$. This notion is important in the context of braid groups, where it has been shown that the closure of quasi-positive braids coincides with the geometrically defined class of $\mathbb{C}$-transverse links. We describe an algorithm that recognizes whether or not an element of a free group is quasi-positive with respect to a basis. Spherical cancellation diagrams over free groups are used to establish the validity of the algorithm and to determine the worst-case runtime. Comment: 15 pages, 2 figures. Revisions: References work of Orevkov; compares his and our methods |
| Databáze: | arXiv |
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