Abstract
A polynomial invariant for multi-knotoids in $S^2$ is given by an elementary and combinatorial method. It is shown that the invariant is an extension of ``a'' HOMFLY polynomial for multi-knotoids and that there exist infinitely many non-trivial knotoids with trivial HOMFLY polynomial. Furthermore, formulas between the polynomials for a given multi-knotoid, its mirror and reverse images are given. By using the formulas, it is revealed that each knotoid with less than four crossings is invertible.
Funding Statement
This work was supported by JSPS KAKENHI Grant number JP17K05255.
Citation
Yasuyuki Miyazawa. "A polynomial invariant for knotoids." Osaka J. Math. 58 (2) 239 - 272, April 2021.
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