Has anyone developed a theory for braids with an infinite number of strings?
$\begingroup$
$\endgroup$
5
-
2$\begingroup$ References here: arxiv.org/pdf/math/0201303v3.pdf $\endgroup$– Francesco PolizziFeb 1, 2016 at 13:21
-
$\begingroup$ See en.wikipedia.org/wiki/… $\endgroup$– JRNMay 18, 2019 at 13:22
-
1$\begingroup$ @JoelReyesNoche Thank you! $\endgroup$– Martin PetersMay 20, 2019 at 7:34
-
$\begingroup$ The infinite strand braid group $B_{\infty}=\bigcup_{n}B_{n}$ has more features and hence a richer theory than the finite strand braid groups. The infinite strand braid group $B_{\infty}$ can be endowed with a self-distributive operation $*$ defined by letting $x*y=x\text{sh}(y)\sigma_{1}\text{sh}(x)^{-1}$ where $\text{sh}:B_{\infty}\rightarrow B_{\infty}$ is the group homomorphism defined by $\text{sh}(\sigma_{i})=\sigma_{i+1}$, and $(B_{\infty},*)$ actually contains the free one generator self-distributive algebra. There is no analogue of this in $B_{n}$. $\endgroup$– Joseph Van NameMay 13, 2021 at 5:00
-
$\begingroup$ @JosephVanName Thanks a lot! Would you have a reference? $\endgroup$– Martin PetersMay 14, 2021 at 8:39
Add a comment
|