
TL;DR
This paper classifies all closed 3-braid diagrams where changing any single crossing results in the same knot or link, revealing a specific class of knots with this property.
Contribution
It provides a complete classification of everywhere equivalent diagrams within the class of closed 3-braids, a novel result in knot theory.
Findings
Identified all closed 3-braid diagrams with the property that crossing changes yield the same knot or link.
Established criteria for when a 3-braid diagram is everywhere equivalent.
Contributed to understanding the symmetry and structure of knots related to crossing modifications.
Abstract
A knot (or link) diagram is said to be everywhere equivalent if all the diagrams obtained by switching one crossing represent the same knot (or link). We classify such diagrams of a closed 3-braid.
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