When is region crossing change an unknotting operation?
Zhiyun Cheng
TL;DR
This paper characterizes when region crossing change can unknot links, showing it is effective if and only if the link is proper, and explores its relation to the Arf invariant.
Contribution
It establishes a precise condition for region crossing change to be an unknotting operation and analyzes its impact on proper links and the Arf invariant.
Findings
Region crossing change is an unknotting operation iff the link is proper.
The behavior of region crossing change on link diagrams is described.
The relation between region crossing change and the Arf invariant is discussed.
Abstract
In this paper, we prove that region crossing change on a link diagram is an unknotting operation if and only if the link is proper. A description of the behavior of region crossing change on link diagrams is given. Furthermore we also discuss the relation between region crossing change and the Arf invariant of proper links.
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