Hard Unknots and Collapsing Tangles
نویسندگان
چکیده
Classical knot theory is about the classification, up to isotopy, of embedded closed curves in three-dimensional space. Two closed curves embedded in three-dimensional space are said to be isotopic if there is a continuous family of embeddings starting with one curve and ending with the other curve. This definition of isotopy captures our intuitive notion of moving a length of elastic rope about in space without tearing it. Given a closed loop of rope in space, it can sometimes be deformed in this way to a simple flat circle. In such a case we say that the loop is unknotted.
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