Knots Are Determined by Their Complements
نویسنده
چکیده
The notion of equivalence of knots can be strengthened by saying that K and K' are isotopic if the above homeomorphism h is isotopic to the identity, or equivalently, orientation-preserving. The analog of Theorem 1 holds in this setting too: if two knots have complements which are homeomorphic by an orientation-preserving homeomorphism, then they are isotopic. Theorem 1 and its orientation-preserving version are easy consequences of the following theorem concerning Dehn surgery.
منابع مشابه
Knots Are Determined by Their Complements
This answers a question apparently first raised by Tietze [T, p. 83]. It was previously known that there were at most two knots with a given complement [CGLS, Corollary 3]. The notion of equivalence of knots can be strengthened by saying that K and K' are isotopic if the above homeomorphism h is isotopic to the identity, or, equivalently, orientation-preserving. The analog of Theorem I holds in...
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