It is known that there exists a surjective map from the set of weak (1, 3) homotopy classes of knot projections to the set of positive knots [N. Ito and Y. Takimura, (1, 2) and weak (1, 3) homotopies on knot projections, J. Knot Theory Ramifications 22 (2013) 1350085]. An interesting question whether this map is also injective, which question was formulated independently by S. Kamada and Y. Nakanishi in 2013 (Question q1). This paper obtains an answer to this question.

中文翻译：

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正结和弱 (1, 3) 同伦

已知存在从节点投影的弱(1, 3)同伦类集合到正节点集合[N. Ito 和 Y. Takimura，(1, 2) 和弱 (1, 3) 节点投影同伦，J. Knot Theory Ramifications 22 (2013) 1350085]。一个有趣的问题是这张地图是否也是单射的，这个问题是由 S. Kamada 和 Y. Nakanishi 在 2013 年独立制定的（问题 q1）。本文得到了这个问题的答案。