turkmath.org

Knotoids are immersed arcs in surfaces, introduced by Vladimir Turaev. Knotoids in the 2-sphere can be considered as open knot diagrams with two endpoints that can lie anywhere in $S^2$. In this sense, the theory of spherical knotoids extends the theory of knots in the Euclidean 3-space, and the classification problem of knots generalizes to knotoids in an interesting way with the existence of open ends. In this talk we will present multi-knotoids and an Alexander polynomial type invariant for them by utilizing a partition function involving a solution of the Yang-Baxter equation. This talk is a joint work with Louis Kauffman.