Pointed quandles of linkoids
arxiv(2024)
摘要
In this paper we define the fundamental quandle of knotoids and linkoids and
prove that it is invariant under the under forbidden-move and hence encodes
only the information of the underclosure of the knotoid. We then introduce
n-pointed quandles, which generalize quandles by specifying n elements as
ordered basepoints. This leads to the notion of fundamental pointed quandles of
linkoids, which enhances the fundamental quandle. Using 2-pointed quandle
allows us to distinguish 1-linkoids with equivalent under-closures and leads to
a couple of 1-linkoid invariants. We also generalize the notion of homogeneity
of quandles to n-homogeneity of quandles. We classify all
∞-homogeneous, finite quandles.
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