A simple torus-like hopfion with hopf charge $Q_H=1$ will typically exhibit a skyrmion at each slice cutting the toroidal circle. What if the skyrmion is replaced by an in-plane 2D vortex, i.e., we set the vector component $S_3=0$ for all such slice skyrmions? Is it still something nontrivial, e.g., what is $Q_H$ now or any other topological index?
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