Knot equivalence refers to the concept in knot theory where two knots are considered equivalent if one can be transformed into the other through a series of allowable deformations, specifically ambient isotopies. This idea is essential in distinguishing between different knots and understanding their properties, as it allows for the classification of knots based on their inherent characteristics rather than their representations. Knot equivalence connects to orientation and chirality, knot diagrams, crossing numbers, and polynomial invariants that help identify or differentiate knots.
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