When is arc crossing change an unknotting operation?

Zhiyun Cheng; Qian Liao; Jingze Song

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arXiv · 2509.08341

When is arc crossing change an unknotting operation?

Zhiyun Cheng·Qian Liao·Jingze Song

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Abstract

This paper extends the study of arc crossing change, a local operation on knot diagrams recently introduced by Cericola, from knot diagrams to link diagrams. We consider two types of arc crossing change on link diagrams and discuss when they are unknotting operations. Furthermore, we show that any two crossing points in an alternating knot diagram are arc crossing change admissible.

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Zhiyun Cheng, Qian Liao, Jingze Song. 2025-09-10. When is arc crossing change an unknotting operation?. https://arxiv.org/abs/2509.08341

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