ambient isotopy

Ambient isotopy is a concept from topology that describes how one shape can be smoothly transformed into another within a space without tearing or cutting. Imagine bending, stretching, or twisting a piece of string or a loop in three-dimensional space; if you can do this without breaking or passing it through itself, the two configurations are considered ambient isotopic. Essentially, it's a way to determine if two knots or shapes are equivalent when allowed to relax and reshape freely in their environment, maintaining their structure throughout the continuous deformation.