C. McA. Gordon, John Luecke
Abstract
Open-access reader
Two (smooth or PL) knots K, K' in S 3 are equivalent if there exists a homeomorphism h: S 3 -• S 3 such that h(K) = K'.This implies that their complements S 3 -K and S 3 -K' are homeomorphic.Here we announce the converse implication.THEOREM 1.If two knots have homeomorphic complements then they are equivalent.
OpenAlex reports 68 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
Two (smooth or PL) knots K, K' in S 3 are equivalent if there exists a homeomorphism h: S 3 -• S 3 such that h(K) = K'.This implies that their complements S 3 -K and S 3 -K' are homeomorphic.Here we announce the converse implication.THEOREM 1.If two knots have homeomorphic complements then they are equivalent.
Key concepts: Mathematics