Realisability of $G_{n}^{3}$, realisability projection, and kernel of the $G_{n}^{3}$-braid presentation
| Autor: | Manturov, Vassily Olegovich |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | The aim of this article is to prove that the kernel of the map from the pure braid group $PB_{n},n\ge 4$ to the group $G_{n}^{3}$ consists of full twist braids and their exponents. The proof consists of two parts. The first part which deals with $n=4$ relies on the crucial tool in this construction having its own interest is the {\em realisability projection} saying that if two {\em realisable} $G_{4}^{3}$-elements are equivalent then they are equivalent by a sequence of realisable ones. The second part (an easy one) uses induction on $n$. Comment: 8 pages |
| Databáze: | arXiv |
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