Abstract:
In [Kim] for an oriented surface $S_{g}$ of genus $g$ it is shown that links in $S_{g} \times S^{1}$ can be presented by virtual diagrams with a decoration, so called, double lines. In this paper, first we define braids with double lines for links in $S_{g}\times S^{1}$. We denote the group of braids with double lines by $VB_{n}^{dl}$. Alexander and Markov theorem for links in $S_{g}\times S^{1}$ can be proved. We show that, if we restrict our interest to the group $B_{n}^{dl}$ generated by braids with double lines, but without virtual crossings, then the Hecke algebra of $B_{n}^{dl}$ is isomorphic to affine Hecke algebra.
Website:
https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09
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