solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看360次
Relating virtual knot invariants to links in $\mathbb{S}^{3}$. (arXiv:1706.07756v1 [math.GT])
来源于:arXiv
Geometric interpretations of some virtual knot invariants are given in terms
of invariants of links in $\mathbb{S}^3$. Alexander polynomials of almost
classical knots are shown to be specializations of the multi-variable Alexander
polynomial of certain two-component boundary links of the form $J \sqcup K$
with $J$ a fibered knot. The index of a crossing, a common ingredient in the
construction of virtual knot invariants, is related to the Milnor triple
linking number of certain three-component links $J \sqcup K_1 \sqcup K_2$ with
$J$ a connected sum of trefoils or figure-eights. Our main technical tool is
virtual covers. This technique, due to Manturov and the first author,
associates a virtual knot $\upsilon$ to a link $J \sqcup K$, where $J$ is
fibered and $\text{lk}(J,K)=0$. Here we extend virtual covers to all
multicomponent links $L=J \sqcup K$, with $K$ a knot. It is shown that an
unknotted component $J_0$ can be added to $L$ so that $J_0 \sqcup J$ is fibered
and $K$ has algebrai 查看全文>>