A note on regular isotopy of singular links (Q2719028)

\textit{H. Whitney} proved in [Compos. Math. 4, 276-284 (1937; Zbl 0016.13804)] that two closed immersed curves in the plane can be homotoped into one another through closed immersed curves if and only if they have the same rotation number. As a generalization of this theorem, it is proved in [\textit{B. Trace}, Proc. Am. Math. Soc. 89, No. 4, 722-724 (1983; Zbl 0554.57003)] that two isotopic oriented knot diagrams are regularly isotopic if and only if they have the same writhe and rotation number.NEWLINENEWLINENEWLINEIn this paper, the author generalizes this result further by showing that two isotopic oriented 4-valent singular link diagrams with transverse intersections are regularly isotopic if and only if they have the same writhe and rotation number. NEWLINENEWLINENEWLINEReviewer's remarks: (1) p. 2500, there is a wrong crossing in the second diagram on the first line. (2) p. 2501, lines 17 and 18, I do not agree with the fact that the two links are not regularly isotopic! It is the same link in both figures!